{"id":32338,"date":"2021-05-09T13:00:48","date_gmt":"2021-05-09T13:00:48","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=32338"},"modified":"2025-03-03T22:26:32","modified_gmt":"2025-03-03T22:26:32","slug":"%d9%85%d8%ac%d8%a7%d9%84%d8%a7%d8%aa-%d8%a7%d9%84%d9%86%d8%b2%d8%a7%d9%87%d8%a9-%d9%88%d8%a7%d9%84%d8%a3%d8%b9%d8%af%d8%a7%d8%af-%d8%a7%d9%84%d8%b5%d8%ad%d9%8a%d8%ad%d8%a9","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%ac%d8%a7%d9%84%d8%a7%d8%aa-%d8%a7%d9%84%d9%86%d8%b2%d8%a7%d9%87%d8%a9-%d9%88%d8%a7%d9%84%d8%a3%d8%b9%d8%af%d8%a7%d8%af-%d8%a7%d9%84%d8%b5%d8%ad%d9%8a%d8%ad%d8%a9\/","title":{"rendered":"\u0645\u062c\u0627\u0644\u0627\u062a \u0627\u0644\u0646\u0632\u0627\u0647\u0629 \u0648\u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0635\u062d\u064a\u062d\u0629"},"content":{"rendered":"<style>\n\tp, ul, ol{\n\ttext-align: justify;\n\t}\n\th1{\n\ttext-align:center;\n\ttext-transform: uppercase;\n\t}\n\th2{\n\ttext-align:center;\n\ttext-transform: uppercase;\n\tfont-size:24pt;\n\t}\n\th3 { \n\t\ttext-align: center;\n\t\ttext-transform: uppercase;\n\t\tfont-size: 24px !important;\n\t}\n<\/style>\n<h1>\u0645\u062c\u0627\u0644\u0627\u062a \u0627\u0644\u0646\u0632\u0627\u0647\u0629 \u0648\u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0635\u062d\u064a\u062d\u0629<\/h1>\n<p style=\"text-align:center;\"><em><strong>\u0645\u0644\u062e\u0635:<\/strong><br \/>\n\t\u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629\u060c \u064a\u062a\u0645 \u062a\u0642\u062f\u064a\u0645 \u0645\u0641\u0647\u0648\u0645 \u0645\u062c\u0627\u0644 \u0627\u0644\u0646\u0632\u0627\u0647\u0629\u060c \u0648\u0634\u0631\u062d \u0623\u0647\u0645\u064a\u062a\u0647 \u0641\u064a \u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u062c\u0628\u0631 \u0627\u0644\u0639\u0627\u0645\u060c \u0648\u0625\u062b\u0628\u0627\u062a \u0628\u0639\u0636 \u062e\u0635\u0627\u0626\u0635\u0647 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\u0627\u0644\u0645\u0634\u062a\u0631\u0643\u0629 \u0628\u064a\u0646 \u0645\u062c\u0627\u0644\u0627\u062a \u0627\u0644\u0646\u0632\u0627\u0647\u0629 \u0648\u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0635\u062d\u064a\u062d\u0629.<\/li>\n<li><strong>\u0625\u062b\u0628\u0627\u062a<\/strong> \u062e\u0635\u0627\u0626\u0635 \u0645\u062c\u0627\u0644\u0627\u062a \u0627\u0644\u0646\u0632\u0627\u0647\u0629 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0628\u0631\u0627\u0647\u064a\u0646 \u0631\u0633\u0645\u064a\u0629.<\/li>\n<\/ol>\n<p style=\"text-align:center;\">\n\t<strong><u>\u0641\u0647\u0631\u0633 \u0627\u0644\u0645\u062d\u062a\u0648\u064a\u0627\u062a<\/u><\/strong><br \/>\n\t<a href=\"#1\">\u0647\u062f\u0641 \u0627\u0644\u062c\u0628\u0631 \u0627\u0644\u0639\u0627\u0645 \u0648\u0627\u0644\u0645\u0639\u0631\u0641\u0629 \u0627\u0644\u0645\u0633\u0628\u0642\u0629<\/a><br \/>\n\t<a href=\"#2\">\u0645\u0646 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0635\u062d\u064a\u062d\u0629 \u0625\u0644\u0649 \u0645\u062c\u0627\u0644\u0627\u062a \u0627\u0644\u0646\u0632\u0627\u0647\u0629<\/a><br \/>\n\t<a href=\"#3\">\u0627\u0644\u062c\u0648\u0627\u0646\u0628 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0627\u0644\u0645\u0634\u062a\u0631\u0643\u0629 \u0628\u064a\u0646 \u0645\u062c\u0627\u0644\u0627\u062a \u0627\u0644\u0646\u0632\u0627\u0647\u0629 \u0648\u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0635\u062d\u064a\u062d\u0629<\/a><br \/>\n\t<a href=\"#4\">\u062e\u0635\u0627\u0626\u0635 \u0645\u062c\u0627\u0644\u0627\u062a \u0627\u0644\u0646\u0632\u0627\u0647\u0629 \u0648\u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0635\u062d\u064a\u062d\u0629<\/a><br \/>\n\t<a href=\"#5\">\u062a\u0645\u0627\u0631\u064a\u0646<\/a>\n<\/p>\n<p><center><br \/>\n\t<iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/hxmc1-eXWxU?si=57GADT52JG4fHFT-\" title=\"\u0645\u0634\u063a\u0644 \u0641\u064a\u062f\u064a\u0648 \u064a\u0648\u062a\u064a\u0648\u0628\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><br \/>\n<\/center><\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u0647\u062f\u0641 \u0627\u0644\u062c\u0628\u0631 \u0627\u0644\u0639\u0627\u0645 \u0648\u0627\u0644\u0645\u0639\u0631\u0641\u0629 \u0627\u0644\u0645\u0633\u0628\u0642\u0629<\/h2>\n<p>\n\t<a href=\"https:\/\/www.youtube.com\/watch?v=hxmc1-eXWxU&amp;t=183s\" target=\"_blank\" rel=\"noopener\"><br \/>\n\t\t<strong><span style=\"color: #ff0000;\">\u0627\u0644\u0647\u062f\u0641 \u0627\u0644\u0631\u0626\u064a\u0633\u064a \u0645\u0646 \u0627\u0644\u062c\u0628\u0631 \u0627\u0644\u0639\u0627\u0645<\/span><\/strong><br \/>\n\t<\/a><br \/>\n\t\u0647\u0648 \u062f\u0631\u0627\u0633\u0629 \u062c\u0645\u064a\u0639 \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0627\u0644\u0645\u0645\u0643\u0646\u0629. \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629\u060c \u0633\u0646\u062f\u0631\u0633 \u0639\u062f\u0629 \u0623\u0646\u0638\u0645\u0629 \u0645\u0646 \u0647\u0630\u0627 \u0627\u0644\u0646\u0648\u0639\u060c \u0648\u0645\u0646 \u0628\u064a\u0646 \u0623\u0647\u0645\u0647\u0627 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0637\u0628\u064a\u0639\u064a\u0629 \u0648\u0627\u0644\u0635\u062d\u064a\u062d\u0629\u060c \u0648\u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u0623\u062e\u064a\u0631\u0629 \u0633\u0646\u0635\u0644 \u0625\u0644\u0649 \u0645\u062c\u0627\u0644\u0627\u062a \u0627\u0644\u0646\u0632\u0627\u0647\u0629.\n<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{N}= \\{1,2,3,4,\\cdots\\}<\/span><\/span><\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{Z}= \\{0,\\pm 1,\\pm 2,\\pm 3,\\pm 4,\\cdots\\}<\/span><\/span><\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u0645\u0646 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0635\u062d\u064a\u062d\u0629 \u0625\u0644\u0649 \u0645\u062c\u0627\u0644\u0627\u062a \u0627\u0644\u0646\u0632\u0627\u0647\u0629<\/h2>\n<p>\n\t<a href=\"https:\/\/www.youtube.com\/watch?v=hxmc1-eXWxU&amp;t=358s\" target=\"_blank\" rel=\"noopener\"><br \/>\n\t\t<strong><span style=\"color: #ff0000;\">\u0633\u0646\u0628\u062f\u0623 \u062f\u0631\u0627\u0633\u062a\u0646\u0627 \u0628\u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0635\u062d\u064a\u062d\u0629\u060c<\/span><\/strong><br \/>\n\t<\/a><br \/>\n\t\u0648\u0627\u0644\u0633\u0628\u0628 \u0641\u064a \u0627\u062a\u0628\u0627\u0639 \u0647\u0630\u0627 \u0627\u0644\u0646\u0647\u062c \u0647\u0648 \u0623\u0646\u0647\u0627 \u062a\u0634\u062a\u0631\u0643 \u0641\u064a \u0623\u0643\u0628\u0631 \u0639\u062f\u062f \u0645\u0646 \u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0645\u0639 \u0645\u0639\u0638\u0645 \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0627\u0644\u062a\u064a \u0633\u0646\u0631\u0627\u062c\u0639\u0647\u0627 \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062f\u0631\u0627\u0633\u0629.\n<\/p>\n<p>\n\t\u0628\u062f\u0644\u0627\u064b de intentar definir qu\u00e9 son los n\u00fameros enteros, iniciaremos suponiendo que, sean lo que sea, satisfacen ciertas propiedades. Para esto se elige un conjunto de axiomas de modo tal que sea posible inferir todas las propiedades que intuitivamente asociamos a los enteros.\n<\/p>\n<p>\n\t\u0643\u0644 \u0647\u0630\u0647 \u0627\u0644\u0623\u0645\u0648\u0631 \u062a\u062a\u0645 \u0645\u0646 \u062e\u0644\u0627\u0644 <strong>\u0645\u0633\u0644\u0645\u0627\u062a \u0628\u064a\u0627\u0646\u0648<\/strong> \u0644\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0637\u0628\u064a\u0639\u064a\u0629 \u0639\u0646\u062f \u0625\u062f\u062e\u0627\u0644 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0644\u0644\u062d\u0633\u0627\u0628. \u0628\u0627\u062a\u0628\u0627\u0639 \u0647\u0630\u0627 \u0627\u0644\u0646\u0647\u062c \u0627\u0644\u0628\u062f\u064a\u0647\u064a \u0648\u062a\u0648\u0633\u064a\u0639 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629 \u0639\u0644\u0649 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0637\u0628\u064a\u0639\u064a\u0629 \u0648\u0627\u0644\u0635\u062d\u064a\u062d\u0629\u060c \u064a\u062a\u0645 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0645\u062c\u0645\u0648\u0639\u0627\u062a \u0639\u062f\u062f\u064a\u0629 \u062c\u062f\u064a\u062f\u0629\u060c \u0645\u062b\u0644 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0646\u0633\u0628\u064a\u0629\u060c \u063a\u064a\u0631 \u0627\u0644\u0646\u0633\u0628\u064a\u0629\u060c \u0627\u0644\u062d\u0642\u064a\u0642\u064a\u0629\u060c \u0627\u0644\u0645\u0631\u0643\u0628\u0629\u060c \u0627\u0644\u0643\u0648\u0627\u062a\u064a\u0631\u0646\u064a\u0648\u0646\u0627\u062a\u060c \u0627\u0644\u0623\u0648\u0643\u062a\u0648\u0646\u064a\u0648\u0646\u0627\u062a\u060c \u0648\u0627\u0644\u0639\u062f\u064a\u062f \u063a\u064a\u0631\u0647\u0627.\n<\/p>\n<p>\n\t\u062b\u0645\u060c \u0625\u0630\u0627 \u0646\u0638\u0631\u0646\u0627 \u0625\u0644\u0649 \u0627\u0644\u0623\u0639\u062f\u0627\u062f 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\u0628\u0627\u0644\u062a\u062d\u062f\u062b \u0639\u0646 \u0643\u0644 \u0647\u0630\u0647 \u0627\u0644\u0645\u062c\u0645\u0648\u0639\u0627\u062a \u0641\u064a \u0648\u0642\u062a \u0648\u0627\u062d\u062f. \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0633\u064a\u0627\u0642\u060c \u062a\u0638\u0647\u0631 \u0645\u0635\u0637\u0644\u062d\u0627\u062a \u0645\u062b\u0644:\n<\/p>\n<ul>\n<li>\u0645\u062c\u0627\u0644 \u0627\u0644\u0646\u0632\u0627\u0647\u0629<\/li>\n<li>\u0627\u0644\u062d\u0644\u0642\u0629<\/li>\n<li>\u0627\u0644\u0645\u062c\u0645\u0648\u0639\u0629<\/li>\n<li>\u0627\u0644\u0641\u0636\u0627\u0621 \u0627\u0644\u0634\u0639\u0627\u0639\u064a<\/li>\n<\/ul>\n<p>\n\t\u0648\u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0627\u0644\u0645\u0635\u0637\u0644\u062d\u0627\u062a \u0627\u0644\u0623\u062e\u0631\u0649 \u0645\u0646 \u0647\u0630\u0627 \u0627\u0644\u0646\u0648\u0639&#8230; \u0633\u0646\u0631\u0643\u0632 \u0637\u0627\u0642\u062a\u0646\u0627 \u0641\u064a \u0627\u0644\u0628\u062f\u0627\u064a\u0629 \u0639\u0644\u0649 \u062f\u0631\u0627\u0633\u0629 <strong>\u0645\u062c\u0627\u0644\u0627\u062a \u0627\u0644\u0646\u0632\u0627\u0647\u0629.<\/strong>\n<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h3>\u0627\u0644\u062c\u0648\u0627\u0646\u0628 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0627\u0644\u0645\u0634\u062a\u0631\u0643\u0629 \u0628\u064a\u0646 \u0645\u062c\u0627\u0644\u0627\u062a \u0627\u0644\u0646\u0632\u0627\u0647\u0629 \u0648\u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0635\u062d\u064a\u062d\u0629<\/h3>\n<p>\n\t<a href=\"https:\/\/www.youtube.com\/watch?v=hxmc1-eXWxU&amp;t=472s\" target=\"_blank\" rel=\"noopener\"><br \/>\n\t\t<strong><span style=\"color: #ff0000;\">\u0644\u0634\u0631\u062d \u0645\u0627 \u0647\u0648 \u0645\u062c\u0627\u0644 \u0627\u0644\u0646\u0632\u0627\u0647\u0629<\/span><\/strong><br \/>\n\t<\/a><br \/>\n\t\u0633\u0646\u0633\u062a\u0639\u064a\u0646 \u0628\u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u062a\u064a \u0646\u0641\u0647\u0645\u0647\u0627 \u062c\u064a\u062f\u064b\u0627 \u0645\u0646 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0635\u062d\u064a\u062d\u0629. \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0633\u064a\u0627\u0642\u060c \u0625\u0630\u0627 \u0643\u0627\u0646 \u0644\u062f\u064a\u0646\u0627 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span>\u060c <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span>\u060c \u0648 <span class=\"katex-eq\" data-katex-display=\"false\">c<\/span> \u0643\u0623\u0639\u062f\u0627\u062f \u0635\u062d\u064a\u062d\u0629\u060c \u0641\u0625\u0646\u0647\u0627 \u062a\u062d\u0642\u0642 <strong>\u0627\u0644\u0642\u0648\u0627\u0646\u064a\u0646<\/strong> \u0627\u0644\u062a\u0627\u0644\u064a\u0629:\n<\/p>\n<ol>\n<li><strong>\u0627\u0644\u0642\u0648\u0627\u0646\u064a\u0646 \u0627\u0644\u062a\u0628\u0627\u062f\u0644\u064a\u0629:<\/strong>\n<ul>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a+b = b + a<\/span><\/span><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">ab = ba<\/span><\/span><\/li>\n<\/ul>\n<\/li>\n<li><strong>\u0627\u0644\u0642\u0648\u0627\u0646\u064a\u0646 \u0627\u0644\u062a\u0631\u0627\u0628\u0637\u064a\u0629:<\/strong>\n<ul>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a+(b+c) = a+b+c = (a+b)+c<\/span><\/span><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(ab)c = abc = a(bc)<\/span><\/span><\/li>\n<\/ul>\n<\/li>\n<li><strong>\u0627\u0644\u0642\u0648\u0627\u0646\u064a\u0646 \u0627\u0644\u062a\u0648\u0632\u064a\u0639\u064a\u0629:<\/strong>\n<ul>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a+(b+c) = a(b+c) = ab+ac<\/span><\/span><\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<p>\n\t\u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0647\u0646\u0627\u0643 \u0628\u0639\u0636 \u0627\u0644\u0639\u0646\u0627\u0635\u0631 \u0627\u0644\u062e\u0627\u0635\u0629 \u0627\u0644\u0645\u0639\u0631\u0648\u0641\u0629 \u0628\u0627\u0644\u0639\u0646\u0627\u0635\u0631 \u0627\u0644\u0645\u062d\u0627\u064a\u062f\u0629.\n<\/p>\n<ul>\n<li><strong>\u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0645\u062d\u0627\u064a\u062f \u0627\u0644\u062c\u0645\u0639\u064a:<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a+ c = a \\leftrightarrow c=0<\/span><\/span><\/li>\n<li><strong>\u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0645\u062d\u0627\u064a\u062f \u0627\u0644\u0636\u0631\u0628\u064a:<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">ac = a \\leftrightarrow c=1<\/span><\/span><\/li>\n<\/ul>\n<p>\n\t\u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0630\u064a \u064a\u0631\u0645\u0632 \u0625\u0644\u064a\u0647 \u0628\u0640 <span class=\"katex-eq\" data-katex-display=\"false\">0<\/span> \u0647\u0648 \u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0645\u062d\u0627\u064a\u062f \u0627\u0644\u062c\u0645\u0639\u064a\u060c \u0648\u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0630\u064a \u064a\u0631\u0645\u0632 \u0625\u0644\u064a\u0647 \u0628\u0640 <span class=\"katex-eq\" data-katex-display=\"false\">1<\/span> \u0647\u0648 \u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0645\u062d\u0627\u064a\u062f \u0627\u0644\u0636\u0631\u0628\u064a.\n<\/p>\n<p>\n\t\u0643\u0645\u0627 \u0623\u0646 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0635\u062d\u064a\u062d\u0629 \u062a\u0645\u062a\u0644\u0643 \u0645\u0642\u0644\u0648\u0628\u0627\u062a \u062c\u0645\u0639\u064a\u0629. \u0644\u0643\u0644 \u0639\u062f\u062f \u0635\u062d\u064a\u062d \u064a\u0648\u062c\u062f \u0645\u0642\u0644\u0648\u0628 \u062c\u0645\u0639\u064a \u0628\u062d\u064a\u062b \u0639\u0646\u062f \u062c\u0645\u0639\u0647\u0645\u0627 \u0646\u062d\u0635\u0644 \u0639\u0644\u0649 \u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0645\u062d\u0627\u064a\u062f \u0627\u0644\u062c\u0645\u0639\u064a.\n<\/p>\n<ul>\n<li><strong>\u0627\u0644\u0645\u0642\u0644\u0648\u0628 \u0627\u0644\u062c\u0645\u0639\u064a:<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a+ c = 0 \\longleftrightarrow c=-a<\/span><\/span><\/li>\n<\/ul>\n<p>\n\t\u064a\u064f\u0639\u0631\u0641 \u0627\u0644\u0645\u0642\u0644\u0648\u0628 \u0627\u0644\u062c\u0645\u0639\u064a \u0628\u0627\u0644\u0625\u0634\u0627\u0631\u0629 \u0627\u0644\u0633\u0627\u0644\u0628\u0629 \u00ab-\u00bb \u0627\u0644\u062a\u064a \u062a\u0631\u0627\u0641\u0642\u0647.\n<\/p>\n<p>\n\t\u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u0647\u0646\u0627\u0643 <strong>\u0642\u0627\u0639\u062f\u0629 \u0627\u0644\u062a\u0628\u0633\u064a\u0637<\/strong> \u0627\u0644\u062a\u064a \u064a\u062a\u0645 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0639\u0646\u0647\u0627 \u0628\u0627\u0644\u0639\u0644\u0627\u0642\u0629:\n<\/p>\n<p style=\"text-align: center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(c\\neq 0 \\wedge ca = cb) \\longleftrightarrow (a=b)<\/span><\/span>\n<\/p>\n<p>\n\t\u0647\u0630\u0647 \u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u062a\u064a \u0627\u0633\u062a\u0639\u0631\u0636\u0646\u0627\u0647\u0627 \u062a\u0646\u0637\u0628\u0642 \u0639\u0644\u0649 \u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0627\u0644\u0645\u062c\u0645\u0648\u0639\u0627\u062a \u0627\u0644\u0623\u062e\u0631\u0649 \u0645\u062b\u0644 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u062d\u0642\u064a\u0642\u064a\u0629\u060c \u0627\u0644\u0645\u0631\u0643\u0628\u0629\u060c \u0643\u062b\u064a\u0631\u0627\u062a \u0627\u0644\u062d\u062f\u0648\u062f\u060c \u0648\u063a\u064a\u0631\u0647\u0627. \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u0646\u0637\u0644\u0642 \u0645\u0635\u0637\u0644\u062d <strong>\u0645\u062c\u0627\u0644 \u0627\u0644\u0646\u0632\u0627\u0647\u0629<\/strong> \u0639\u0644\u0649 \u062c\u0645\u064a\u0639 \u0627\u0644\u0645\u062c\u0645\u0648\u0639\u0627\u062a \u0627\u0644\u062a\u064a \u062a\u062d\u0642\u0642 \u0647\u0630\u0647 \u0627\u0644\u062e\u0635\u0627\u0626\u0635.\n<\/p>\n<p>\n\t<span style=\"color: #800000;\"><strong>\u0627\u0644\u062a\u0639\u0631\u064a\u0641:<\/strong><\/span> \u0645\u062c\u0627\u0644 \u0627\u0644\u0646\u0632\u0627\u0647\u0629 \u0647\u0648 \u0623\u064a \u0645\u062c\u0645\u0648\u0639\u0629 <span class=\"katex-eq\" data-katex-display=\"false\">D<\/span> \u0645\u0632\u0648\u062f\u0629 \u0628\u0639\u0645\u0644\u064a\u062a\u064a \u0627\u0644\u062c\u0645\u0639 \u0648\u0627\u0644\u0636\u0631\u0628 \u0628\u062d\u064a\u062b:\n<\/p>\n<ul>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a,b\\in D \\longrightarrow a+b \\in D<\/span><\/span><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a,b\\in D \\longrightarrow ab \\in D<\/span><\/span><\/li>\n<\/ul>\n<p>\n\t\u0648\u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u064a\u062a\u0645 \u062a\u062d\u0642\u064a\u0642 \u0627\u0644\u0642\u0648\u0627\u0646\u064a\u0646 <strong>\u0627\u0644\u062a\u0631\u0627\u0628\u0637\u064a\u0629\u060c \u0648\u0627\u0644\u062a\u0628\u0627\u062f\u0644\u064a\u0629\u060c<\/strong> \u0648<strong>\u0627\u0644\u062a\u0648\u0632\u064a\u0639\u064a\u0629\u060c<\/strong> \u0643\u0645\u0627 \u064a\u062d\u062a\u0648\u064a <span class=\"katex-eq\" data-katex-display=\"false\">D<\/span> \u0639\u0644\u0649 <strong>\u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0645\u062d\u0627\u064a\u062f \u0627\u0644\u062c\u0645\u0639\u064a<\/strong> \u0648<strong>\u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0645\u062d\u0627\u064a\u062f \u0627\u0644\u0636\u0631\u0628\u064a<\/strong> (\u0648\u0643\u0644\u0627\u0647\u0645\u0627 \u0641\u0631\u064a\u062f)\u060c \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u062a\u062a\u062d\u0642\u0642 <strong>\u0642\u0627\u0639\u062f\u0629 \u0627\u0644\u062a\u0628\u0633\u064a\u0637.<\/strong>\n<\/p>\n<h4>\u0645\u062b\u0627\u0644 \u0639\u0644\u0649 \u0645\u062c\u0627\u0644 \u0627\u0644\u0646\u0632\u0627\u0647\u0629<\/h4>\n<p>\n\t<a href=\"https:\/\/www.youtube.com\/watch?v=hxmc1-eXWxU&amp;t=749s\" target=\"_blank\" rel=\"noopener\"><br \/>\n\t\t<strong><span style=\"color: #ff0000;\">\u0644\u0646\u0646\u0638\u0631 \u0625\u0644\u0649 \u0627\u0644\u0645\u062c\u0645\u0648\u0639\u0629 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A=\\{a+b\\sqrt{3}\\; |\\; a,b\\in \\mathbb{Z}\\}.<\/span><\/span><\/span><\/strong><br \/>\n\t<\/a><br \/>\n\t\u0647\u0630\u0647 \u0627\u0644\u0645\u062c\u0645\u0648\u0639\u0629\u060c \u0639\u0646\u062f \u062a\u0632\u0648\u064a\u062f\u0647\u0627 \u0628\u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u062c\u0645\u0639 \u0648\u0627\u0644\u0636\u0631\u0628 \u0627\u0644\u0645\u0639\u062a\u0627\u062f\u0629\u060c \u062a\u064f\u0639\u062f \u0645\u062c\u0627\u0644 \u0646\u0632\u0627\u0647\u0629 \u0644\u0623\u0646\u0647\u0627 \u062a\u062d\u0642\u0642 \u0642\u0648\u0627\u0646\u064a\u0646 \u0627\u0644\u062a\u0628\u0627\u062f\u0644\u060c \u0627\u0644\u062a\u0631\u0627\u0628\u0637\u060c \u0648\u0627\u0644\u062a\u0648\u0632\u064a\u0639\u060c \u0648\u062a\u062d\u062a\u0648\u064a \u0639\u0644\u0649 \u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0645\u062d\u0627\u064a\u062f \u0627\u0644\u062c\u0645\u0639\u064a \u0648\u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0645\u062d\u0627\u064a\u062f \u0627\u0644\u0636\u0631\u0628\u064a\u060c \u0648\u0623\u064a\u0636\u064b\u0627 \u062a\u0645\u062a\u0644\u0643 \u0645\u0642\u0644\u0648\u0628\u064b\u0627 \u062c\u0645\u0639\u064a\u064b\u0627.\n<\/p>\n<ul>\n<li><strong>\u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0645\u062d\u0627\u064a\u062f \u0627\u0644\u062c\u0645\u0639\u064a:<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0+0\\sqrt{3}<\/span><\/span><\/li>\n<li><strong>\u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0645\u062d\u0627\u064a\u062f \u0627\u0644\u0636\u0631\u0628\u064a:<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1+0\\sqrt{3}<\/span><\/span><\/li>\n<li><strong>\u0627\u0644\u0645\u0642\u0644\u0648\u0628 \u0627\u0644\u062c\u0645\u0639\u064a:<\/strong> \u0643\u0644 \u0639\u0646\u0635\u0631 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a+b\\sqrt{3}<\/span><\/span> \u0644\u0647 \u0645\u0642\u0644\u0648\u0628 \u062c\u0645\u0639\u064a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-a-b\\sqrt{3}<\/span><\/span><\/li>\n<\/ul>\n<p>\n\t\u0648\u0627\u0644\u0623\u0645\u0631 \u0627\u0644\u0623\u0643\u062b\u0631 \u0623\u0647\u0645\u064a\u0629 \u0647\u0648 \u0623\u0646 \u0647\u0630\u0647 \u0627\u0644\u0645\u062c\u0645\u0648\u0639\u0629 A \u0645\u063a\u0644\u0642\u0629 \u062a\u062d\u062a \u0639\u0645\u0644\u064a\u062a\u064a \u0627\u0644\u062c\u0645\u0639 \u0648\u0627\u0644\u0636\u0631\u0628\u060c \u0628\u0645\u0639\u0646\u0649 \u0623\u0646\u0647 \u0625\u0630\u0627 \u0623\u062e\u0630\u0646\u0627 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x,y\\in A<\/span><\/span> \u0641\u0625\u0646\u0647 \u0633\u064a\u0643\u0648\u0646 \u0644\u062f\u064a\u0646\u0627 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x+y\\in A<\/span><\/span> \u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">xy\\in A.<\/span><\/span><br \/>\n\t\u0647\u0630\u0627 \u0645\u0646 \u0627\u0644\u0633\u0647\u0644 \u0627\u0644\u062a\u062d\u0642\u0642 \u0645\u0646\u0647: \u0625\u0630\u0627 \u0643\u0627\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a_1 + b_1\\sqrt{3}<\/span><\/span> \u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a_2 + b_2\\sqrt{3}<\/span><\/span> \u0639\u0646\u0635\u0631\u064a\u0646 \u0641\u064a <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span>\u060c \u0641\u0625\u0646\u0646\u0627 \u0646\u062d\u0635\u0644 \u0639\u0644\u0649:\n<\/p>\n<p style=\"text.align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n\t(a_1 + b_1\\sqrt{3}) + (a_2 + b_2\\sqrt{3}) &amp;=(a_1+a_2) + (b_1 + b_2)\\sqrt{3} \\in A\\\\ \\\\\n\n\t(a_1 + b_1\\sqrt{3})  (a_2 + b_2\\sqrt{3})  &amp;= a_1a_2 + a_1b_2\\sqrt{3}+b_1a_2\\sqrt{3} + 3b_1b_2 \\\\\n\n\t&amp;=(a_1a_2 + 3b_1b_2) + (a_1b_2 + b_1a_2)\\sqrt{3} \\in A\n\n\t\\end{array}<\/span>\n<p>\t<center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/y6jXNPhjKv4?si=9SaXhWHN42sC73lZ\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/center><\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h3>\u062e\u0635\u0627\u0626\u0635 \u0645\u062c\u0627\u0644\u0627\u062a \u0627\u0644\u0646\u0632\u0627\u0647\u0629 \u0648\u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0635\u062d\u064a\u062d\u0629<\/h3>\n<h4>\u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0645\u062d\u0627\u064a\u062f \u0627\u0644\u062c\u0645\u0639\u064a \u0641\u064a \u0645\u062c\u0627\u0644 \u0627\u0644\u0646\u0632\u0627\u0647\u0629 \u0641\u0631\u064a\u062f \u0645\u0646 \u0646\u0648\u0639\u0647<\/h4>\n<p>\n\t<a href=\"https:\/\/www.youtube.com\/watch?v=y6jXNPhjKv4&amp;t=26s\" target=\"_blank\" rel=\"noopener\"><br \/>\n\t\t<strong><span style=\"color: #ff0000;\">\u064a\u0645\u0643\u0646 \u0625\u062b\u0628\u0627\u062a \u0630\u0644\u0643 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u0628\u0627\u0644\u062e\u0644\u0641:<\/span><\/strong><br \/>\n\t<\/a><br \/>\n\t\u0644\u0646\u0641\u0631\u0636 \u0623\u0646 \u0647\u0646\u0627\u0643 \u0639\u0646\u0635\u0631\u064a\u0646 \u0645\u062d\u0627\u064a\u062f\u064a\u0646 \u062c\u0645\u0639\u064a\u064a\u0646\u060c \u0648\u0644\u064a\u0643\u0646 <span class=\"katex-eq\" data-katex-display=\"false\">0<\/span> \u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0^\\prime<\/span><\/span> \u0639\u0646\u0635\u0631\u064a\u0646 \u0645\u062d\u0627\u064a\u062f\u064a\u0646 \u062c\u0645\u0639\u064a\u064a\u0646. \u0639\u0646\u062f\u0647\u0627 \u0633\u064a\u0643\u0648\u0646 \u0644\u062f\u064a\u0646\u0627:\n<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\">\n\t<span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n\t(1) &amp; 0\\neq 0^\\prime &amp; \\text{; \u0641\u0631\u0636\u064a\u0629}\\\\\n\n\t(2) &amp; a+0 = a &amp; \\text{; \u0641\u0631\u0636\u064a\u0629: $0$ \u0647\u0648 \u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0645\u062d\u0627\u064a\u062f \u0627\u0644\u062c\u0645\u0639\u064a}\\\\\n\n\t(3) &amp; b+0^\\prime = b &amp; \\text{; \u0641\u0631\u0636\u064a\u0629: $0^\\prime$ \u0647\u0648 \u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0645\u062d\u0627\u064a\u062f \u0627\u0644\u062c\u0645\u0639\u064a}\\\\\n\n\t(4) &amp; 0^\\prime + 0 = 0^\\prime &amp; \\text{; \u0628\u062a\u0628\u062f\u064a\u0644 $a=0^\\prime$ \u0641\u064a $(2)$}\\\\\n\n\t(5) &amp; 0 + 0^\\prime = 0 &amp; \\text{; \u0628\u062a\u0628\u062f\u064a\u0644 $b=0$ \u0641\u064a $(3)$}\\\\\n\n\t(6) &amp; 0 = 0^\\prime  &amp; \\text{; \u0645\u0646 $(4,5)$ \u0648\u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062a\u0628\u0627\u062f\u0644\u064a\u0629 \u0627\u0644\u062c\u0645\u0639}\\\\\n\n\t(7) &amp; \\bot &amp;\\text{; \u0645\u0646 $(1,6)$}\n\n\t\\end{array}<\/span>\n<\/p>\n<p>\u0645\u0646 \u0647\u0630\u0627 \u0627\u0644\u0627\u0633\u062a\u0646\u062a\u0627\u062c\u060c \u0646\u0633\u062a\u0646\u062a\u062c \u0623\u0646\u0647:<\/p>\n<p style=\"text-align:center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{0 \\neq 0^\\prime, a + 0 = a, b + 0^\\prime = b\\}\\vdash \\bot.<\/span><\/span>\n<\/p>\n<p>\u0648\u0645\u0646 \u062b\u0645\u060c \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u0628\u0627\u0644\u062e\u0644\u0641\u060c \u0646\u062d\u0635\u0644 \u0639\u0644\u0649:<\/p>\n<p style=\"text-align:center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{a + 0 = a, b + 0^\\prime = b\\}\\vdash 0 = 0^\\prime.<\/span><\/span>\n<\/p>\n<p>\u0623\u064a \u0623\u0646\u0647 \u0625\u0630\u0627 \u0648\u064f\u062c\u062f \u0639\u0646\u0635\u0631\u0627\u0646 \u0645\u062d\u0627\u064a\u062f\u0627\u0646 \u062c\u0645\u0639\u064a\u0627\u0646\u060c \u0641\u0625\u0646\u0647\u0645\u0627 \u064a\u0643\u0648\u0646\u0627\u0646 \u0645\u062a\u0637\u0627\u0628\u0642\u064a\u0646\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0645\u062d\u0627\u064a\u062f \u0627\u0644\u062c\u0645\u0639\u064a \u0641\u0631\u064a\u062f.<\/p>\n<h4>\u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0645\u062d\u0627\u064a\u062f \u0627\u0644\u0636\u0631\u0628\u064a \u0623\u064a\u0636\u064b\u0627 \u0641\u0631\u064a\u062f<\/h4>\n<p>\n\t<a href=\"https:\/\/www.youtube.com\/watch?v=y6jXNPhjKv4&amp;t=305s\" target=\"_blank\" rel=\"noopener\"><br \/>\n\t\t<strong><span style=\"color: #ff0000;\">\u0627\u0644\u0625\u062b\u0628\u0627\u062a \u0645\u0634\u0627\u0628\u0647 \u062a\u0645\u0627\u0645\u064b\u0627 \u0644\u0645\u0627 \u0633\u0628\u0642.<\/span><\/strong><br \/>\n\t<\/a><br \/>\n\t\u0625\u0630\u0627 \u0643\u0627\u0646 \u0647\u0646\u0627\u0643 \u0639\u0646\u0635\u0631\u0627\u0646 \u0645\u062d\u0627\u064a\u062f\u0627\u0646 \u0636\u0631\u0628\u064a\u0627\u064b\u060c \u0648\u0644\u064a\u0643\u0646 <span class=\"katex-eq\" data-katex-display=\"false\">1<\/span> \u0648 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1^\\prime<\/span><\/span>\u060c \u0641\u0625\u0646\u0647 \u064a\u0645\u0643\u0646 \u0625\u062c\u0631\u0627\u0621 \u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u0627\u0644\u062a\u0627\u0644\u064a:\n<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\">\n\t<span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n\t(1) &amp; 1\\neq 1^\\prime &amp; \\text{; \u0641\u0631\u0636\u064a\u0629}\\\\\n\n\t(2) &amp; 1\\cdot a = a &amp; \\text{; \u0641\u0631\u0636\u064a\u0629: $1$ \u0647\u0648 \u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0645\u062d\u0627\u064a\u062f \u0627\u0644\u0636\u0631\u0628\u064a}\\\\\n\n\t(3) &amp; 1^\\prime \\cdot b = b &amp; \\text{; \u0641\u0631\u0636\u064a\u0629: $1^\\prime$ \u0647\u0648 \u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0645\u062d\u0627\u064a\u062f \u0627\u0644\u0636\u0631\u0628\u064a}\\\\\n\n\t(4) &amp; 1\\cdot 1^\\prime = 1^\\prime &amp; \\text{; \u0628\u062a\u0628\u062f\u064a\u0644 $a=1^\\prime$ \u0641\u064a $(2)$}\\\\\n\n\t(5) &amp; 1^\\prime \\cdot 1 = 1 &amp; \\text{; \u0628\u062a\u0628\u062f\u064a\u0644 $b=1$ \u0641\u064a $(3)$}\\\\\n\n\t(6) &amp; 1 = 1^\\prime  &amp; \\text{; \u0645\u0646 $(4,5)$ \u0648\u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062a\u0628\u0627\u062f\u0644\u064a\u0629 \u0627\u0644\u0636\u0631\u0628}\\\\\n\n\t(7) &amp; \\bot &amp;\\text{; \u0645\u0646 $(1,6)$}\n\n\t\\end{array}<\/span>\n<\/p>\n<p>\u0648\u0628\u0630\u0644\u0643 \u0646\u0633\u062a\u0646\u062a\u062c \u0623\u0646:<\/p>\n<p style=\"text-align:center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\{1 \\neq 1^\\prime, 1a= a, 1b = b\\}\\vdash \\bot.<\/span><\/span>\n<\/p>\n<p>\u062b\u0645\u060c \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u0628\u0627\u0644\u062e\u0644\u0641\u060c \u0646\u062d\u0635\u0644 \u0639\u0644\u0649:<\/p>\n<p style=\"text-align:center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{1a= a, 1b= b\\}\\vdash 1 = 1^\\prime.<\/span><\/span>\n<\/p>\n<p>\u0623\u064a \u0623\u0646\u0647 \u0625\u0630\u0627 \u0648\u064f\u062c\u062f \u0639\u0646\u0635\u0631\u0627\u0646 \u0645\u062d\u0627\u064a\u062f\u0627\u0646 \u0636\u0631\u0628\u064a\u0627\u064b\u060c \u0641\u0625\u0646\u0647\u0645\u0627 \u064a\u0643\u0648\u0646\u0627\u0646 \u0645\u062a\u0637\u0627\u0628\u0642\u064a\u0646\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0645\u062d\u0627\u064a\u062f \u0627\u0644\u0636\u0631\u0628\u064a \u0641\u0631\u064a\u062f.<\/p>\n<h4>\u062a\u0646\u0637\u0628\u0642 \u0642\u0627\u0639\u062f\u0629 \u0627\u0644\u062a\u0628\u0633\u064a\u0637 \u0639\u0644\u0649 \u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u062c\u0645\u0639<\/h4>\n<p>\n\t<a href=\"https:\/\/www.youtube.com\/watch?v=y6jXNPhjKv4&amp;t=461s\" target=\"_blank\" rel=\"noopener\"><br \/>\n\t\t<strong><span style=\"color: #ff0000;\">\u0647\u0630\u0627 \u0647\u0648 \u0645\u0627 \u0646\u0642\u0648\u0645 \u0628\u0647 \u0639\u0646\u062f\u0645\u0627<\/span><\/strong><br \/>\n\t<\/a><br \/>\n\t\u0646\u062d\u0630\u0641 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0645\u062a\u0634\u0627\u0628\u0647\u0629 \u0641\u064a \u0645\u0639\u0627\u062f\u0644\u0629:\n<\/p>\n<p style=\"text-align:center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a+b = a+c \\longleftrightarrow b = c<\/span><\/span>\n<\/p>\n<p>\u0644\u064a\u0633 \u0645\u0646 \u0627\u0644\u0635\u0639\u0628 \u0625\u062b\u0628\u0627\u062a \u0647\u0630\u0647 \u0627\u0644\u0646\u062a\u064a\u062c\u0629\u060c \u062d\u064a\u062b \u064a\u0643\u0641\u064a \u0627\u062a\u0628\u0627\u0639 \u0627\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\">\n\t<span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n\t(1) &amp; a+b = a+c &amp; \\text{; \u0641\u0631\u0636\u064a\u0629} \\\\\n\n\t(2) &amp; a+b-a = a+c-a &amp; \\text{; \u0645\u0646$(1)$\u060c \u0628\u0625\u0636\u0627\u0641\u0629 $-a$ \u0625\u0644\u0649 \u0627\u0644\u0637\u0631\u0641\u064a\u0646} \\\\\n\n\t(3) &amp; (a-a)+b = (a-a)+c &amp; \\text{; \u0645\u0646$(2)$\u060c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062a\u0628\u0627\u062f\u0644\u064a\u0629 \u0648\u0627\u0644\u062a\u0631\u0627\u0628\u0637\u064a\u0629} \\\\\n\n\t(4) &amp; 0+b = 0+c &amp; \\text{; \u0645\u0646$(3)$\u060c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0645\u0642\u0644\u0648\u0628 \u0627\u0644\u062c\u0645\u0639\u064a} \\\\\n\n\t(5) &amp; b = c &amp; \\text{; \u0645\u0646$(4)$\u060c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0645\u062d\u0627\u064a\u062f \u0627\u0644\u062c\u0645\u0639\u064a} \\\\\n\n\t\\end{array}<\/span>\n<\/p>\n<p>\n\t\u0648\u0628\u0645\u0627 \u0623\u0646 \u0647\u0630\u0627 \u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u064a\u0645\u0643\u0646 \u0639\u0643\u0633\u0647 \u0628\u062a\u0637\u0628\u064a\u0642 \u0646\u0641\u0633 \u0627\u0644\u062e\u0637\u0648\u0627\u062a\u060c \u0641\u0625\u0646\u0647 \u064a\u0646\u062a\u062c \u0644\u062f\u064a\u0646\u0627:\n<\/p>\n<p style=\"text-align: center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a+b=a+c \\dashv \\vdash b=c<\/span><\/span>\n<\/p>\n<p>\u0648\u0647\u0630\u0627 \u0645\u0643\u0627\u0641\u0626 \u0644\u0644\u0642\u0648\u0644:<\/p>\n<p style=\"text-align: center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdash a+b=a+c \\longleftrightarrow b=c<\/span><\/span>\n<\/p>\n<h4>\u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0645\u062d\u0627\u064a\u062f \u0627\u0644\u062c\u0645\u0639\u064a \u0647\u0648 \u0623\u064a\u0636\u064b\u0627 \u0639\u0646\u0635\u0631 \u0645\u0645\u062a\u0635 \u0641\u064a \u0627\u0644\u0636\u0631\u0628<\/h4>\n<p>\n\t<a href=\"https:\/\/www.youtube.com\/watch?v=y6jXNPhjKv4&amp;t=632s\" target=\"_blank\" rel=\"noopener\"><br \/>\n\t\t<strong><span style=\"color: #ff0000;\">\u0628\u0628\u0633\u0627\u0637\u0629\u060c \u0647\u0630\u0627 \u064a\u0639\u0646\u064a<\/span><\/strong><br \/>\n\t<\/a><br \/>\n\t\u0623\u0646\u0647 \u0644\u0643\u0644 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span> \u0641\u064a \u0645\u062c\u0627\u0644 \u0627\u0644\u0646\u0632\u0627\u0647\u0629\u060c \u064a\u062a\u062d\u0642\u0642 \u0623\u0646:\n<\/p>\n<p style=\"text-align:center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a\\cdot 0 = 0<\/span><\/span>\n<\/p>\n<p>\u0648\u064a\u0645\u0643\u0646 \u0625\u062b\u0628\u0627\u062a \u0630\u0644\u0643 \u0628\u0633\u0647\u0648\u0644\u0629 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u062a\u0628\u0627\u0639 \u0627\u0644\u062a\u0633\u0644\u0633\u0644 \u0627\u0644\u0645\u0646\u0637\u0642\u064a \u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\">\n\t<span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n\t(1) &amp; a\\cdot a + a\\cdot 0 = a\\cdot  (a+0) &amp; \\text{; \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0642\u0627\u0646\u0648\u0646 \u0627\u0644\u062a\u0648\u0632\u064a\u0639}\\\\\n\n\t(2) &amp; a\\cdot a + a\\cdot 0 = a\\cdot  (a+a-a) &amp; \\text{; \u0645\u0646$(1)$\u060c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0645\u0642\u0644\u0648\u0628 \u0627\u0644\u062c\u0645\u0639\u064a}\\\\\n\n\t(3) &amp; a\\cdot a + a\\cdot 0 = a\\cdot a + a\\cdot a - a\\cdot a &amp; \\text{; \u0645\u0646$(2)$\u060c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0642\u0627\u0646\u0648\u0646 \u0627\u0644\u062a\u0648\u0632\u064a\u0639}\\\\\n\n\t(4) &amp;  a\\cdot 0 =  a\\cdot a - a\\cdot a &amp; \\text{; \u0645\u0646$(3)$\u060c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0642\u0627\u0639\u062f\u0629 \u0627\u0644\u062a\u0628\u0633\u064a\u0637 \u0641\u064a \u0627\u0644\u062c\u0645\u0639}\\\\\n\n\t(5) &amp;  a\\cdot 0 =  0 &amp; \\text{; \u0645\u0646$(4)$\u060c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0645\u0642\u0644\u0648\u0628 \u0627\u0644\u062c\u0645\u0639\u064a}\\\\\n\n\t\\end{array}<\/span>\n<\/p>\n<h4><strong>\u0642\u0627\u0639\u062f\u0629 \u0627\u0644\u0625\u0634\u0627\u0631\u0627\u062a:<\/strong><\/h4>\n<p>\n\t<a href=\"https:\/\/www.youtube.com\/watch?v=y6jXNPhjKv4&amp;t=736s\" target=\"_blank\" rel=\"noopener\"><br \/>\n\t\t<strong><span style=\"color: #ff0000;\">\u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0643\u0645\u064a\u062a\u064a\u0646 \u0644\u0647\u0645\u0627 \u0646\u0641\u0633 \u0627\u0644\u0625\u0634\u0627\u0631\u0629<\/span><\/strong><br \/>\n\t<\/a><br \/>\n\t\u062f\u0627\u0626\u0645\u064b\u0627 \u064a\u0643\u0648\u0646 \u0645\u0648\u062c\u0628\u064b\u0627\u061b \u0641\u064a \u062d\u064a\u0646 \u0623\u0646 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0643\u0645\u064a\u062a\u064a\u0646 \u0628\u0625\u0634\u0627\u0631\u062a\u064a\u0646 \u0645\u062a\u0639\u0627\u0643\u0633\u062a\u064a\u0646 \u064a\u0643\u0648\u0646 \u062f\u0627\u0626\u0645\u064b\u0627 \u0633\u0627\u0644\u0628\u064b\u0627. \u064a\u0645\u0643\u0646 \u0625\u062b\u0628\u0627\u062a \u0647\u0630\u0647 \u0627\u0644\u062e\u0627\u0635\u064a\u0629 \u0628\u0633\u0647\u0648\u0644\u0629 \u0623\u064a\u0636\u064b\u0627:\n<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\">\n\t<span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n\t(1) &amp; a\\cdot b = a\\cdot b + 0 &amp; \\text{; \u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0645\u062d\u0627\u064a\u062f \u0627\u0644\u062c\u0645\u0639\u064a}\\\\\n\n\t(2) &amp; a\\cdot b = a\\cdot b + (a)\\cdot(-b) - (a)\\cdot(-b) &amp; \\text{; \u0645\u0646 $(1)$ \u0648\u0627\u0644\u0645\u0642\u0644\u0648\u0628 \u0627\u0644\u062c\u0645\u0639\u064a}\\\\\n\n\t(3) &amp; a\\cdot b = a\\cdot (b -b) - (a)\\cdot(-b) &amp; \\text{; \u0645\u0646 $(2)$ \u0648\u0627\u0644\u0645\u0642\u0644\u0648\u0628 \u0627\u0644\u062c\u0645\u0639\u064a}\\\\\n\n\t(4) &amp; a\\cdot b = a\\cdot 0 + (-a)\\cdot(-b) &amp; \\text{; \u0645\u0646 $(3)$ \u0648\u0627\u0644\u0645\u0642\u0644\u0648\u0628 \u0627\u0644\u062c\u0645\u0639\u064a}\\\\\n\n\t(5) &amp; a\\cdot b = (-a)\\cdot(-b) &amp; \\text{; \u0645\u0646 $(4)$ \u0648\u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0645\u0645\u062a\u0635 \u0641\u064a \u0627\u0644\u0636\u0631\u0628}\\\\\n\n\t\\end{array}<\/span>\n<\/p>\n<p>\u0648\u0628\u0630\u0644\u0643 \u0646\u062d\u0635\u0644 \u0639\u0644\u0649: <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> ab = (-a)(-b)<\/span><\/span><\/p>\n<p>\u0648\u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0639\u0644\u0627\u0645\u0627\u062a \u0627\u0644\u0645\u062a\u0639\u0627\u0643\u0633\u0629\u060c \u064a\u0643\u0648\u0646 \u0627\u0644\u0627\u0633\u062a\u0646\u062a\u0627\u062c \u0645\u0645\u0627\u062b\u0644\u0627\u064b:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\">\n\t<span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n\t(1) &amp; a\\cdot(-b) = a \\cdot (-b) + 0 &amp; \\text{; \u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0645\u062d\u0627\u064a\u062f \u0627\u0644\u062c\u0645\u0639\u064a} \\\\\n\n\t(2) &amp; a\\cdot(-b) = a \\cdot (-b) + a \\cdot b  -  a \\cdot b  &amp; \\text{; \u0645\u0646 $(1)$ \u0648\u0627\u0644\u0645\u0642\u0644\u0648\u0628 \u0627\u0644\u062c\u0645\u0639\u064a} \\\\\n\n\t(3) &amp; a\\cdot(-b) = a \\cdot (b-b)  -  a \\cdot b  &amp; \\text{; \u0645\u0646 $(2)$ \u0648\u0627\u0644\u062a\u0648\u0632\u064a\u0639\u064a\u0629} \\\\\n\n\t(4) &amp; a\\cdot(-b) = a \\cdot 0  -  a \\cdot b  &amp; \\text{; \u0645\u0646 $(3)$ \u0648\u0627\u0644\u0645\u0642\u0644\u0648\u0628 \u0627\u0644\u062c\u0645\u0639\u064a} \\\\\n\n\t(5) &amp; a\\cdot(-b) = - a \\cdot b  &amp; \\text{; \u0645\u0646 $(4)$ \u0648\u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0645\u0645\u062a\u0635 \u0641\u064a \u0627\u0644\u0636\u0631\u0628} \\\\\n\n\t\\end{array}<\/span>\n<\/p>\n<p>\u0648\u0628\u0630\u0644\u0643 \u0646\u062d\u0635\u0644 \u0639\u0644\u0649: <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a(-b) = -a(b)<\/span><\/span><\/p>\n<h4>\u0625\u0630\u0627 \u0643\u0627\u0646 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0639\u062f\u062f\u064a\u0646 \u064a\u0633\u0627\u0648\u064a \u0635\u0641\u0631\u064b\u0627\u060c \u0641\u0625\u0646 \u0648\u0627\u062d\u062f\u064b\u0627 \u0645\u0646\u0647\u0645\u0627 \u0639\u0644\u0649 \u0627\u0644\u0623\u0642\u0644 \u064a\u0633\u0627\u0648\u064a \u0635\u0641\u0631\u064b\u0627<\/h4>\n<p>\n\t<a href=\"https:\/\/www.youtube.com\/watch?v=y6jXNPhjKv4&amp;t=875s\" target=\"_blank\" rel=\"noopener\"><br \/>\n\t\t<strong><span style=\"color: #ff0000;\">\u062e\u0627\u0635\u064a\u0629 \u0623\u062e\u0631\u0649 \u062a\u064f\u0633\u062a\u062e\u062f\u0645 \u0643\u062b\u064a\u0631\u064b\u0627<\/span><\/strong><br \/>\n\t<\/a><br \/>\n\t\u0647\u064a \u0627\u0644\u062a\u0627\u0644\u064a\u0629:\n<\/p>\n<p style=\"text-align: center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">ab=0 \\leftrightarrow (a=0 \\vee b=0)<\/span><\/span>\n<\/p>\n<p>\u0648\u064a\u0645\u0643\u0646 \u0625\u062b\u0628\u0627\u062a\u0647\u0627 \u0628\u0633\u0647\u0648\u0644\u0629 \u0623\u064a\u0636\u064b\u0627:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\">\n\t<span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n\t(1) &amp; \\{a=0\\} \\models a\\cdot b = 0  &amp; \\textbf{; \u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0645\u0645\u062a\u0635 \u0641\u064a \u0627\u0644\u0636\u0631\u0628} \\\\\n\n\t(2) &amp; \\models a=0 \\rightarrow a\\cdot b = 0  &amp;\\text{; TD$(1)$} \\\\\n\n\t(3) &amp; \\models \\neg (a\\cdot b = 0 ) \\rightarrow \\neg(a=0) &amp;\\text{; CPI$(2)$} \\\\\n\n\t(4) &amp; \\{\\neg (a\\cdot b = 0 ) \\}\\models   \\neg(a=0) &amp;\\text{; RTD$(3)$} \\\\\n\n\t(5) &amp; \\{\\neg (a\\cdot b = 0 ) \\}\\models   \\neg(b=0) &amp;\\text{; \u0645\u0645\u0627\u062b\u0644\u0629 $(4)$} \\\\\n\n\t(6) &amp; \\{\\neg (a\\cdot b = 0 ) \\}\\models  \\neg(a=0) \\wedge \\neg(b=0) &amp;\\text{; $\\wedge$-int$(4,5)$} \\\\\n\n\t(7) &amp; \\models (\\neg (a\\cdot b = 0 )) \\rightarrow \\neg(a=0) \\wedge \\neg(b=0)  &amp;\\text{; TD(6)} \\\\\n\n\t(8) &amp; \\models \\neg(\\neg(a=0) \\wedge \\neg(b=0) ) \\rightarrow   (a\\cdot b = 0 ) &amp;\\text{; CPI(7)} \\\\\n\n\t(9) &amp; \\models (a=0 \\vee b=0) \\rightarrow   (a\\cdot b = 0 ) &amp;\\text{; DM(8)} \\\\\n\n\t(10)&amp; \\{a\\neq 0 , a\\cdot b=0\\} \\models b=0 &amp; \\textbf{; \u0627\u0644\u0639\u0646\u0635\u0631 \u0627\u0644\u0645\u0645\u062a\u0635 \u0641\u064a \u0627\u0644\u0636\u0631\u0628} \\\\\n\n\t(11)&amp; \\{a\\cdot b=0\\} \\models a\\neq 0 \\rightarrow  b=0 &amp; \\text{; TD(10)} \\\\\n\n\t(12)&amp; \\{a\\cdot b=0\\} \\models \\neg(a\\neq 0) \\vee  b=0 &amp; \\text{; $\\rightarrow$-Def(11)} \\\\\n\n\t(13)&amp; \\{a\\cdot b=0\\} \\models a=0 \\vee  b=0 &amp; \\text{; DN(12)} \\\\\n\n\t(14)&amp; \\models (a\\cdot b=0) \\rightarrow (a=0 \\vee  b=0) &amp; \\text{; TD(13)} \\\\\n\n\t(15)&amp; \\models (a\\cdot b=0) \\leftrightarrow (a=0 \\vee  b=0) &amp; \\text{; \u0645\u0646$(9,14)$}\n\n\t\\end{array}<\/span>\n<\/p>\n<p><center><br \/>\n\t<iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/KZQ3PXeMlKk?si=O_Hek5KFG853Q6qT\" title=\"\u0645\u0634\u063a\u0644 \u0641\u064a\u062f\u064a\u0648 \u064a\u0648\u062a\u064a\u0648\u0628\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><br \/>\n<\/center><\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u062a\u0645\u0627\u0631\u064a\u0646<\/h2>\n<p>\u0644\u062a\u0643\u0646 <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span>\u060c <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u0648 <span class=\"katex-eq\" data-katex-display=\"false\">c<\/span> \u0639\u0646\u0627\u0635\u0631 \u062a\u0646\u062a\u0645\u064a \u0625\u0644\u0649 \u0645\u062c\u0627\u0644 \u0646\u0632\u0627\u0647\u0629 <span class=\"katex-eq\" data-katex-display=\"false\">D<\/span>. \u0623\u062b\u0628\u062a \u0623\u0646 \u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u062a\u062a\u062d\u0642\u0642:<\/p>\n<ol>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(-a)=(-1)a<\/span><\/span><br \/>\n\t\t<a href=\"https:\/\/www.youtube.com\/watch?v=KZQ3PXeMlKk&amp;t=306s\" target=\"_blank\" rel=\"noopener\"><br \/>\n\t\t\t<strong><span style=\"color: #ff0000;\">[\u0627\u0644\u062d\u0644]<\/span><\/strong><br \/>\n\t\t<\/a>\n\t<\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-(a+b)=(-a) + (-b)<\/span><\/span><br \/>\n\t\t<a href=\"https:\/\/www.youtube.com\/watch?v=KZQ3PXeMlKk&amp;t=827s\" target=\"_blank\" rel=\"noopener\"><br \/>\n\t\t\t<strong><span style=\"color: #ff0000;\">[\u0627\u0644\u062d\u0644]<\/span><\/strong><br \/>\n\t\t<\/a>\n\t<\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a(-b)=-(ab)<\/span><\/span><br \/>\n\t\t<a href=\"https:\/\/www.youtube.com\/watch?v=KZQ3PXeMlKk&amp;t=1213s\" target=\"_blank\" rel=\"noopener\"><br \/>\n\t\t\t<strong><span style=\"color: #ff0000;\">[\u0627\u0644\u062d\u0644]<\/span><\/strong><br \/>\n\t\t<\/a>\n\t<\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-(-a)=a<\/span><\/span><br \/>\n\t\t<a href=\"https:\/\/www.youtube.com\/watch?v=KZQ3PXeMlKk&amp;t=1628s\" target=\"_blank\" rel=\"noopener\"><br \/>\n\t\t\t<strong><span style=\"color: #ff0000;\">[\u0627\u0644\u062d\u0644]<\/span><\/strong><br \/>\n\t\t<\/a>\n\t<\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a(b-c) = ab - ac<\/span><\/span> <strong>[\u0645\u0642\u062a\u0631\u062d]<\/strong><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(a-b)+(b-c) = a-c<\/span><\/span> <strong>[\u0645\u0642\u062a\u0631\u062d]<\/strong><\/li>\n<li>\u0644\u0643\u0644 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a\\in D<\/span><\/span> \u064a\u0648\u062c\u062f \u0639\u062f\u062f \u0648\u062d\u064a\u062f <span class=\"katex-eq\" data-katex-display=\"false\">1<\/span> \u0628\u062d\u064a\u062b<br \/>\n\t\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a\\cdot 1 = a<\/span><\/span><br \/>\n\t\t<a href=\"https:\/\/www.youtube.com\/watch?v=KZQ3PXeMlKk&amp;t=2029s\" target=\"_blank\" rel=\"noopener\"><br \/>\n\t\t\t<strong><span style=\"color: #ff0000;\">[\u0627\u0644\u062d\u0644]<\/span><\/strong><br \/>\n\t\t<\/a>\n\t<\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">xx = x \\leftrightarrow (x=1 \\vee x=0)<\/span><\/span> <strong>[\u0645\u0642\u062a\u0631\u062d]<\/strong><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u0645\u062c\u0627\u0644\u0627\u062a \u0627\u0644\u0646\u0632\u0627\u0647\u0629 \u0648\u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0635\u062d\u064a\u062d\u0629 \u0645\u0644\u062e\u0635: \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629\u060c \u064a\u062a\u0645 \u062a\u0642\u062f\u064a\u0645 \u0645\u0641\u0647\u0648\u0645 \u0645\u062c\u0627\u0644 \u0627\u0644\u0646\u0632\u0627\u0647\u0629\u060c \u0648\u0634\u0631\u062d \u0623\u0647\u0645\u064a\u062a\u0647 \u0641\u064a \u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u062c\u0628\u0631 \u0627\u0644\u0639\u0627\u0645\u060c \u0648\u0625\u062b\u0628\u0627\u062a \u0628\u0639\u0636 \u062e\u0635\u0627\u0626\u0635\u0647 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0628\u0631\u0627\u0647\u064a\u0646 \u0631\u0633\u0645\u064a\u0629. \u0623\u0647\u062f\u0627\u0641 \u0627\u0644\u062a\u0639\u0644\u0645: \u0639\u0646\u062f \u0625\u0643\u0645\u0627\u0644 \u0647\u0630\u0647 \u0627\u0644\u062d\u0635\u0629\u060c \u0633\u064a\u0643\u0648\u0646 \u0627\u0644\u0637\u0627\u0644\u0628 \u0642\u0627\u062f\u0631\u064b\u0627 \u0639\u0644\u0649: \u0641\u0647\u0645 \u0647\u062f\u0641 \u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u062c\u0628\u0631 \u0627\u0644\u0639\u0627\u0645. \u0641\u0647\u0645 \u0645\u0641\u0647\u0648\u0645 \u0645\u062c\u0627\u0644 \u0627\u0644\u0646\u0632\u0627\u0647\u0629. \u0634\u0631\u062d \u0627\u0644\u062c\u0648\u0627\u0646\u0628 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0627\u0644\u0645\u0634\u062a\u0631\u0643\u0629 \u0628\u064a\u0646 \u0645\u062c\u0627\u0644\u0627\u062a \u0627\u0644\u0646\u0632\u0627\u0647\u0629 \u0648\u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0635\u062d\u064a\u062d\u0629. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":32317,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":6,"footnotes":""},"categories":[1037,565],"tags":[],"class_list":["post-32338","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-1037","category-565"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u0645\u062c\u0627\u0644\u0627\u062a \u0627\u0644\u0646\u0632\u0627\u0647\u0629 \u0648\u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0635\u062d\u064a\u062d\u0629 - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u0627\u0633\u062a\u0643\u0634\u0641 \u0645\u062c\u0627\u0644\u0627\u062a \u0627\u0644\u0646\u0632\u0627\u0647\u0629 \u0641\u064a \u0627\u0644\u062c\u0628\u0631\u060c \u062e\u0635\u0627\u0626\u0635\u0647\u0627 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