\u0938\u0902\u0916\u094d\u092f\u093e \u0938\u092e\u0941\u091a\u094d\u091a\u092f\u094b\u0902 \u0915\u0940 \u092a\u0939\u0932\u0940 \u092a\u0939\u091a\u093e\u0928 – ToposUranos.com<\/title> <\/head> <body> <\/p>\n<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>\u0938\u0902\u0916\u094d\u092f\u093e \u0938\u092e\u0941\u091a\u094d\u091a\u092f\u094b\u0902 \u0915\u0940 \u092a\u0939\u0932\u0940 \u092a\u0939\u091a\u093e\u0928: \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0947 \u091c\u091f\u093f\u0932 \u0924\u0915<\/h1>\n<\/center><\/p>\n\u0938\u093e\u0930\u093e\u0902\u0936:<\/strong><\/br>\u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0939\u092e \u091c\u093e\u0902\u091a\u0947\u0902\u0917\u0947 \u0915\u093f \u0915\u0948\u0938\u0947 \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 \u0905\u0928\u094d\u092f \u0938\u0902\u0916\u094d\u092f\u093e \u0938\u092e\u0941\u091a\u094d\u091a\u092f\u094b\u0902 \u0915\u0947 \u0928\u093f\u0930\u094d\u092e\u093e\u0923 \u0915\u0947 \u0906\u0927\u093e\u0930 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0909\u092a\u092f\u094b\u0917 \u0915\u0940 \u091c\u093e \u0938\u0915\u0924\u0940 \u0939\u0948\u0902 \u0924\u093e\u0915\u093f \u0935\u0947 \u0915\u0941\u091b \u0938\u0902\u091a\u093e\u0932\u0928\u0940\u092f \u0938\u0940\u092e\u093e\u0913\u0902 \u0915\u094b \u092a\u093e\u0930 \u0915\u0930 \u0938\u0915\u0947\u0902\u0964 \u0939\u092e \u092a\u0942\u0930\u094d\u0923 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0938\u0947 \u0936\u0941\u0930\u0942 \u0915\u0930\u0947\u0902\u0917\u0947, \u091c\u094b \u0939\u092e\u0947\u0902 \u0935\u094d\u092f\u093e\u092a\u0915 \u0930\u0942\u092a \u0938\u0947 \u0918\u091f\u093e\u0935 \u0915\u0930\u0928\u0947 \u0915\u0940 \u0905\u0928\u0941\u092e\u0924\u093f \u0926\u0947\u0924\u0947 \u0939\u0948\u0902\u0964 \u092b\u093f\u0930, \u0939\u092e \u092a\u0930\u093f\u092e\u0947\u092f \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0940 \u0913\u0930 \u092c\u0922\u093c\u0947\u0902\u0917\u0947, \u091c\u094b \u0939\u092e\u0947\u0902 \u092a\u0942\u0930\u0940 \u0924\u0930\u0939 \u0938\u0947 \u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u093e \u0909\u092a\u0915\u0930\u0923 \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964 \u092c\u093e\u0926 \u092e\u0947\u0902, \u0939\u092e \u0928-\u0935\u093e\u0902 \u092e\u0942\u0932\u094b\u0902 \u0915\u0947 \u0938\u093e\u0925 \u0915\u093e\u092e \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u092e\u0947\u0902 \u092a\u094d\u0930\u0935\u0947\u0936 \u0915\u0930\u0947\u0902\u0917\u0947, \u0914\u0930 \u0939\u092e \u091a\u0930\u094d\u091a\u093e \u0915\u0930\u0947\u0902\u0917\u0947 \u0915\u093f \u0915\u0948\u0938\u0947 \u091c\u091f\u093f\u0932 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 \u0928-\u0935\u093e\u0902 \u092e\u0942\u0932\u094b\u0902 \u0915\u0947 \u0935\u093f\u0936\u093f\u0937\u094d\u091f \u092a\u0930\u093f\u092a\u094d\u0930\u0947\u0915\u094d\u0937\u094d\u092f\u094b\u0902 \u0915\u094b \u0938\u0902\u092d\u094b\u0927\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092a\u0930\u093f\u091a\u092f\u093f\u0924 \u0915\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948\u0902\u0964 \u0907\u0928 \u0935\u093f\u0915\u093e\u0938\u094b\u0902 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947, \u0938\u092e\u091d\u093e \u091c\u093e\u090f\u0917\u093e \u0915\u093f \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0928\u0908 \u0938\u0902\u0916\u094d\u092f\u093e \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u092a\u0942\u0930\u094d\u0935\u0935\u0930\u094d\u0924\u0940 \u0915\u0947 \u0905\u0902\u0924\u0930\u094d\u0928\u093f\u0939\u093f\u0924 \u0938\u092e\u0938\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u0939\u0932 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u0948\u0938\u0947 \u0909\u0924\u094d\u092a\u0928\u094d\u0928 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/em><\/p>\n\u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0947 \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f<\/u>:<\/strong> \u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u0915\u094b \u0938\u092e\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u0947 \u092a\u0930 \u091b\u093e\u0924\u094d\u0930 \u0938\u0915\u094d\u0937\u092e \u0939\u094b\u0917\u093e:<\/p>\n<ol>\n<li>\u092a\u0939\u091a\u093e\u0928\u0928\u093e<\/strong> \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915, \u092a\u0942\u0930\u094d\u0923 \u0914\u0930 \u092a\u0930\u093f\u092e\u0947\u092f \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0940 \u092e\u094c\u0932\u093f\u0915 \u0917\u0941\u0923\u0935\u0924\u094d\u0924\u093e\u090f\u0901\u0964<\/li>\n<li>\u0935\u094d\u092f\u093e\u0916\u094d\u092f\u093e \u0915\u0930\u0928\u093e<\/strong> \u0935\u0947 \u0917\u0941\u0923\u0935\u0924\u094d\u0924\u093e\u090f\u0901 \u0914\u0930 \u0938\u0902\u091a\u093e\u0932\u0928 \u091c\u094b \u090f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0915\u094b \u0909\u0938\u0915\u0947 \u0905\u0917\u0932\u0947 \u092e\u0947\u0902 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u093f\u0924 \u0915\u0930 \u0926\u0947\u0924\u0947 \u0939\u0948\u0902\u0964<\/li>\n<li>\u0924\u0941\u0932\u0928\u093e \u0915\u0930\u0928\u093e<\/strong> \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0938\u0902\u0916\u094d\u092f\u093e \u0938\u092e\u0941\u091a\u094d\u091a\u092f\u094b\u0902 \u0915\u0940 \u0917\u0941\u0923\u0935\u0924\u094d\u0924\u093e\u090f\u0901 \u0914\u0930 \u092f\u0947 \u0915\u0948\u0938\u0947 \u090f\u0915 \u0926\u0942\u0938\u0930\u0947 \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0939\u0948\u0902\u0964<\/li>\n<\/ol>\n\u0938\u093e\u092e\u0917\u094d\u0930\u0940 \u0938\u0942\u091a\u0940<\/u><\/strong> \n<a href=\"#1\">\u092a\u0930\u093f\u091a\u092f<\/a> \n<a href=\"#2\">\u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0940 \u0917\u0941\u0923\u0935\u0924\u094d\u0924\u093e\u090f\u0901<\/a> \n<a href=\"#3\">\u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0938\u0947 \u092a\u0942\u0930\u094d\u0923 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u092e\u0947\u0902 \u092a\u093e\u0930\u093e\u0935\u0943\u0924\u094d\u0924\u093f<\/a> \n<a href=\"#4\">\u092a\u0930\u093f\u092e\u0947\u092f \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u092e\u0947\u0902 \u091c\u0902\u092a<\/a> \n<a href=\"#5\">\u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0914\u0930 \u0905\u0924\u0930\u094d\u0915\u093f\u0924 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901<\/a> \n<a href=\"#6\">\u091c\u091f\u093f\u0932: \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0940 \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u0909\u092a\u091c<\/a>\n<\/p>\n<center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/PfK-pIlyCj4\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center>\n<\/div>\n<a name=\"1\"><\/a><\/p>\n<h2>\u092a\u0930\u093f\u091a\u092f<\/h2>\n<div class=\"content\">\n<a href=\"https:\/\/www.youtube.com\/watch?v=PfK-pIlyCj4&t=96s\" target=\"_blank\" rel=\"noopener\">\u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901, \u091c\u093f\u0928\u094d\u0939\u0947\u0902 \u0939\u092e \u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0905\u0928\u094d\u0935\u0947\u0937\u0923 \u0915\u0930\u0947\u0902\u0917\u0947,<\/strong><\/span><\/a> \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u0935\u093f\u0938\u094d\u0924\u093e\u0930 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u092a\u0930\u093f\u091a\u092f\u093f\u0924 \u0915\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948\u0902\u0964 \u0910\u0938\u093e \u0939\u094b\u0924\u093e \u0939\u0948 \u0915\u093f, \u0915\u093f\u0938\u0940 \u092d\u0940 \u0926\u094b \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u0938\u093e\u0925, \u0939\u092e\u0947\u0936\u093e \u0918\u091f\u093e\u0935 \u092f\u093e \u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u0940 \u0938\u0902\u091a\u093e\u0932\u0928 \u0915\u0930\u0928\u093e \u0938\u0902\u092d\u0935 \u0928\u0939\u0940\u0902 \u0939\u0948, \u0914\u0930 \u0907\u0928 \u0935\u093f\u0938\u094d\u0924\u093e\u0930\u094b\u0902 \u0915\u093e \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f \u0907\u0938 \u0938\u092e\u0938\u094d\u092f\u093e \u0915\u093e \u0938\u092e\u093e\u0927\u093e\u0928 \u0915\u0930\u0928\u093e \u0939\u0948\u0964<\/p>\n\u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u0915\u0947 \u0926\u094c\u0930\u093e\u0928, \u0939\u092e <a href=\"https:\/\/toposuranos.com\/operaciones-con-numeros-naturales\/\" rel=\"noopener\" target=\"_blank\">\u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u0938\u0902\u091a\u093e\u0932\u0928 \u0914\u0930 \u0917\u0941\u0923\u0935\u0924\u094d\u0924\u093e<\/strong><\/a> \u0915\u0940 \u0938\u092e\u0940\u0915\u094d\u0937\u093e \u0915\u0930\u0947\u0902\u0917\u0947, \u0914\u0930 \u0907\u0938 \u0906\u0927\u093e\u0930 \u092a\u0930, \u0939\u092e \u0938\u092d\u0940 \u0905\u0928\u094d\u092f \u0938\u0902\u0916\u094d\u092f\u093e \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0940 \u0928\u093f\u0930\u094d\u092e\u093e\u0923 \u0915\u0940 \u0913\u0930 \u092c\u0922\u093c\u0947\u0902\u0917\u0947, \u091c\u092c \u0924\u0915 \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0924\u0915 \u092a\u0939\u0941\u0902\u091a \u0928\u0939\u0940\u0902 \u091c\u093e\u0924\u0947 \u0914\u0930 \u0909\u0938\u0938\u0947 \u092d\u0940 \u0906\u0917\u0947\u0964<\/p>\n<a name=\"2\"><\/a><\/p>\n<h2>\u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0940 \u0917\u0941\u0923\u0935\u0924\u094d\u0924\u093e<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=PfK-pIlyCj4&t=214s\" target=\"_blank\" rel=\"noopener\">\u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u0938\u0902\u091a\u093e\u0932\u0928 \u0915\u094b \u0938\u092e\u091d\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f,<\/span><\/strong><\/a> \u0939\u092e \u092e\u0941\u0916\u094d\u092f \u0930\u0942\u092a \u0938\u0947 \u091c\u094b\u0921\u093c \u0914\u0930 \u0909\u0924\u094d\u092a\u093e\u0926 \u0915\u0940 \u0913\u0930 \u0938\u0902\u0926\u0930\u094d\u092d\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u0938\u093e\u0925 \u0939\u0940 \u0909\u0928\u0915\u0947 \u092a\u094d\u0930\u0924\u093f\u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0938\u0902\u091a\u093e\u0932\u0928\u0964 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u092e\u0947\u0902 \u0907\u0928 \u0917\u0941\u0923\u0935\u0924\u094d\u0924\u093e\u0913\u0902 \u0915\u093e \u0938\u0902\u0915\u094d\u0937\u0947\u092a \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948:<\/p>\n\u091a\u0942\u0902\u0915\u093f a,b,c\\in\\mathbb{N},<\/span> \u092f\u0939 \u0938\u0924\u094d\u092f \u0939\u0948 \u0915\u093f:<\/p>\n<table>\n<tbody>\n<tr style=\"text-align: justify; color: #000000;\">\n<td>1. <\/td>\n<td>a + b = b + a<\/span>\n<\/td>\n<\/tr>\n<tr style=\"text-align: left; color: #000000;\">\n<td>2. <\/td>\n<td>a \\pm (b \\pm c) = (a\\pm b)\\pm c <\/span> (\u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937\u0923 \u0915\u0947 \u092e\u093e\u092e\u0932\u0947 \u092e\u0947\u0902, \u092f\u0939 \u0938\u0926\u0948\u0935 \u0938\u0924\u094d\u092f \u0939\u0948 \u091c\u092c \u092f\u0939 \u0938\u0939\u0940 \u0930\u0942\u092a \u0938\u0947 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0939\u094b)\n<\/td>\n<\/tr>\n<tr style=\"text-align: left; color: #000000;\">\n<td>3. <\/td>\n<td>a\\cdot b = b \\cdot a <\/span>\n<\/td>\n<\/tr>\n<tr style=\"text-align: left; color: #000000;\">\n<td>4. <\/td>\n<td>a\\cdot(b\\cdot c)= (a\\cdot b)\\cdot c <\/span>\n<\/td>\n<\/tr>\n<tr style=\"text-align: left; color: #000000;\">\n<td>5.\\;\\;\\;\\;\\;<\/span><\/td>\n<td>a\\cdot b = a \\leftrightarrow b=1 <\/span>\n<\/td>\n<\/tr>\n<tr style=\"text-align: left; color: #000000;\">\n<td>6.<\/td>\n<td>\\displaystyle \\frac{a}{b}\\in\\mathbb{N} \\leftrightarrow (\\exists k\\in\\mathbb{N})(a=b\\cdot k) <\/span>\n<\/td>\n<\/tr>\n<tr style=\"text-align: left; color: #000000;\">\n<td>7.<\/td>\n<td>a\\cdot(b+c)=a\\cdot b + a \\cdot c <\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<a name=\"3\"><\/a><\/p>\n<h2>\u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0938\u0947 \u092a\u0942\u0930\u094d\u0923 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u092e\u0947\u0902 \u092a\u093e\u0930\u093e\u0935\u0943\u0924\u094d\u0924\u093f<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=PfK-pIlyCj4&t=418s\" target=\"_blank\" rel=\"noopener\">\u092a\u0939\u0932\u0940 \u092c\u093e\u0924 \u091c\u093f\u0938\u0947 \u0927\u094d\u092f\u093e\u0928 \u092e\u0947\u0902 \u0930\u0916\u0928\u093e \u0939\u0948, \u092f\u0939 \u0939\u0948 \u0915\u093f \u091c\u094b\u0921\u093c \u0915\u0947 \u092e\u093e\u092e\u0932\u0947 \u092e\u0947\u0902:<\/span><\/strong><\/a> (\\forall a,b\\in\\mathbb{N})(a+b\\in\\mathbb{N})<\/span>, \u091c\u092c\u0915\u093f \u0918\u091f\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f: (\\forall a,b\\in\\mathbb{N})(a+b\\in\\mathbb{N} \\leftrightarrow a\\gt b)<\/span>. \u090f\u0915 \u0938\u092e\u0938\u094d\u092f\u093e \u0924\u092c \u0909\u0924\u094d\u092a\u0928\u094d\u0928 \u0939\u094b\u0924\u0940 \u0939\u0948 \u091c\u092c \u0926\u094b \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 a<\/span> \u0914\u0930 b<\/span> \u0915\u0947 \u092c\u0940\u091a \u0915\u0940 \u0918\u091f\u093e\u0928\u093e \u092e\u093e\u092f\u0928\u0947 \u0928\u0939\u0940\u0902 \u0930\u0916\u0924\u0940 \u0905\u0917\u0930 a\\leq b<\/span>; \u0907\u0938 \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u094b \u0938\u0941\u0927\u093e\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u092a\u0942\u0930\u094d\u0923 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u0938\u092e\u0942\u0939 \u092e\u0947\u0902 \u0935\u093f\u0938\u094d\u0924\u093e\u0930\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u091c\u0939\u093e\u0902 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u0940 \u0918\u091f\u093e\u0928\u093e \u0915\u094b \u0905\u091a\u094d\u091b\u0940 \u0924\u0930\u0939 \u0938\u0947 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u092e\u093e\u0928 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0939\u092e \u0907\u0938 \u0928\u0908 \u0938\u092e\u0942\u0939 \u0915\u094b \u092a\u0942\u0930\u094d\u0923 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901<\/strong> \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u091a\u093f\u0939\u094d\u0928\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902 \\mathbb{Z}<\/span>, \u0914\u0930 \u092f\u0939 \u0938\u092d\u0940 \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902, \u0909\u0928\u0915\u0947 \u092f\u094b\u0917\u093f\u0915 \u0935\u093f\u092a\u0930\u0940\u0924 \u0914\u0930 \u0936\u0942\u0928\u094d\u092f \u0938\u0947 \u092e\u093f\u0932\u0915\u0930 \u092c\u0928\u0924\u093e \u0939\u0948\u0964<\/p>\n\\mathbb{Z} = \\{\\cdots, -3,-2,-1,0,1,2,3,\\cdots \\}<\/span>\n\u092a\u0942\u0930\u094d\u0923 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u0938\u092d\u0940 \u0917\u0941\u0923\u094b\u0902 \u0914\u0930 \u0938\u0902\u091a\u093e\u0930\u094b\u0902 \u0915\u094b \u0905\u0927\u093f\u0917\u094d\u0930\u0939\u0923 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u0926\u0942\u0938\u0930\u0947 \u0917\u0941\u0923 \u092a\u0930 \u090f\u0915 \u0935\u093f\u0938\u094d\u0924\u093e\u0930 \u0915\u0947 \u0938\u093e\u0925, \u0914\u0930 \u092f\u094b\u0917\u093f\u0915 \u0935\u093f\u092a\u0930\u0940\u0924 \u0914\u0930 \u092f\u094b\u0917\u093f\u0915 \u0924\u091f\u0938\u094d\u0925 \u0915\u0940 \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u090f\u0901 \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948\u0902\u0964<\/p>\n<table>\n<tbody>\n<tr style=\"text-align: left; color: #000000;\">\n<td>2*.<\/td>\n<td>a \\pm (b \\pm c) = (a\\pm b) \\pm c <\/span><\/td>\n<\/tr>\n<tr style=\"text-align: left; color: #000000;\">\n<td>8.<\/td>\n<td>(\\forall a\\in\\mathbb{Z})(\\exists ! b\\in\\mathbb{Z})(a+b=0 \\leftrightarrow b=-a)<\/span><\/td>\n<\/tr>\n<tr style=\"text-align: left; color: #000000;\">\n<td>9.<\/td>\n<td>(\\forall a\\in\\mathbb{Z})(\\exists ! b\\in\\mathbb{Z})(a+b=a \\leftrightarrow b=0)<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\u0924\u0924\u094d\u0935 b=-a<\/span> \u0935\u0939 \u0939\u0948 \u091c\u093f\u0938\u0947 \u0939\u092e a<\/span> \u0915\u093e \u092f\u094b\u0917\u093f\u0915 \u0935\u093f\u092a\u0930\u0940\u0924<\/strong> \u0915\u0939\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<a name=\"4\"><\/a><\/p>\n<h2>\u0930\u093e\u0936\u0928\u0932 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u092e\u0947\u0902 \u0909\u091b\u093e\u0932<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=PfK-pIlyCj4&t=755s\" target=\"_blank\" rel=\"noopener\">\u0907\u0938 \u092c\u093f\u0902\u0926\u0941 \u092a\u0930 \u090f\u0915\u092e\u093e\u0924\u094d\u0930 \u0911\u092a\u0930\u0947\u0936\u0928 \u091c\u094b \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u0938\u0939\u0940 \u0924\u0930\u0940\u0915\u0947 \u0938\u0947 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0928\u0939\u0940\u0902 \u0939\u0948, \u0935\u0939 \u0935\u093f\u092d\u093e\u091c\u0928 \u0939\u0948\u0964<\/span><\/strong><\/a> \u0907\u0938\u0947 \u0939\u0932 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0939\u092e \u092a\u0942\u0930\u094d\u0923 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u0938\u092e\u0942\u0939 \u092e\u0947\u0902 \u0935\u093f\u0938\u094d\u0924\u093e\u0930 \u0915\u0930\u0947\u0902\u0917\u0947 \u091c\u094b \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u092e\u0942\u0939 \u0926\u094d\u0935\u093e\u0930\u093e \u0926\u093f\u092f\u093e \u091c\u093e\u090f\u0917\u093e:<\/p>\n\\mathbb{Q}=\\left\\{a= \\displaystyle\\frac{n}{m}\\;|\\;n,m\\in\\mathbb{Z}\\wedge m\\neq 0 \\right\\}<\/span>\n\u0907\u0938\u0938\u0947 \u090f\u0915 \u0928\u0908 \u092a\u094d\u0930\u0949\u092a\u0930\u094d\u091f\u0940 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u0940 \u0939\u0948<\/p>\n<table>\n<tbody>\n<tr style=\"text-align: justify; color: #000000;\">\n<td>10.<\/td>\n<td>(\\forall a \\in \\mathbb{Q}\\setminus\\{0\\})(\\exists ! b \\in \\mathbb{Q})<\/span> \\left[(a\\cdot b = 1) \\leftrightarrow \\left( b = \\displaystyle \\frac{1}{a} = a^{-1} \\right)\\right]<\/span><\/td>\n<\/tr>\n<tr style=\"text-align: justify; color: #000000;\">\n<td colspan=\"2\">\u0939\u0930 \u0905-\u0936\u0942\u0928\u094d\u092f \u0930\u093e\u0936\u0928\u0932 \u092e\u0947\u0902 \u090f\u0915 \u0917\u0941\u0923\u091c \u0909\u0932\u094d\u091f\u093e \u0939\u094b\u0924\u093e \u0939\u0948\u0964 a<\/span> \u0915\u093e \u0917\u0941\u0923\u091c \u0909\u0932\u094d\u091f\u093e a^{-1}<\/span> \u0939\u0948<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\u0907\u0928 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902, \u0911\u092a\u0930\u0947\u0936\u0928\u094d\u0938 \u0914\u0930 \u092a\u094d\u0930\u0949\u092a\u0930\u094d\u091f\u0940\u091c \u0915\u0947 \u0938\u093e\u0925 \u0928\u090f \u0911\u092a\u0930\u0947\u0936\u0928\u094d\u0938 \u0914\u0930 \u0909\u0928\u0915\u0940 \u092a\u094d\u0930\u0949\u092a\u0930\u094d\u091f\u0940\u091c \u0915\u094b \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u092e\u0947\u0902 \u090f\u0915 \u0930\u093e\u0936\u0928\u0932 q<\/span> \u0915\u0940 \u0928-\u0935\u0940\u0902 \u0936\u0915\u094d\u0924\u093f \u0915\u094b \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0926\u094d\u0935\u093e\u0930\u093e<\/p>\nq^n = \\underbrace{q\\cdot q \\cdot \\cdots \\cdot q}_{n\\;\u092c\u093e\u0930};<\/span> \u0938\u093e\u0925 n\\in\\mathbb{N}<\/span>\nq^{-n}= \\displaystyle \\frac{1}{q^n}<\/span>\n\u0927\u094d\u092f\u093e\u0928 \u0926\u0947\u0902 \u0915\u093f, \u0907\u0938\u0938\u0947, \u0914\u0930 \u091c\u092c \u0924\u0915 q\\neq 0<\/span> \u0939\u0948, \u0939\u092e \u0915\u0939 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f<\/p>\nq^0 = 1<\/span>\n\u0907\u0938\u0915\u0947 \u0905\u0932\u093e\u0935\u093e, \u091c\u092c \u092d\u0940 \u0936\u0942\u0928\u094d\u092f \u0938\u0947 \u0935\u093f\u092d\u093e\u091c\u0928 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902, \u0926\u094b \u0930\u093e\u0936\u0928\u0932\u094d\u0938 a,b<\/span> \u0914\u0930 \u0926\u094b \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915 n,m<\/span> \u0915\u0947 \u0932\u093f\u090f \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u092a\u094d\u0930\u0949\u092a\u0930\u094d\u091f\u0940\u091c \u092e\u093e\u0928\u094d\u092f \u0939\u094b\u0924\u0940 \u0939\u0948\u0902:<\/p>\n<table>\n<tbody>\n<tr style=\"text-align: justify; color: #000000;\">\n<td>11.<\/td>\n<td>a^n \\cdot a^m = a^{n+m} <\/span>\n<\/td>\n<\/tr>\n<tr style=\"text-align: justify; color: #000000;\">\n<td>12.<\/td>\n<td>(a^n)^m = a^{n\\cdot m} <\/span>\n<\/td>\n<\/tr>\n<tr style=\"text-align: justify; color: #000000;\">\n<td>13.<\/td>\n<td>(a\\cdot b)^n = a^{n} \\cdot a^{m} <\/span>\n<\/td>\n<\/tr>\n<tr style=\"text-align: justify; color: #000000;\">\n<td>14.<\/td>\n<td>\\left(\\displaystyle \\frac{a}{a}\\right)^n = \\frac{a^n}{a^n} <\/span>\n<\/td>\n<\/tr>\n<tr style=\"text-align: justify; color: #000000;\">\n<td>15.<\/td>\n<td>\\displaystyle \\frac{a^n}{a^m} = a^{n-m} = \\frac{1}{a^{m-n}} <\/span>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<a name=\"5\"><\/a><\/p>\n<h2>\u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0914\u0930 \u0905\u0924\u0930\u094d\u0915\u0938\u0902\u0916\u094d\u092f\u093e<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=PfK-pIlyCj4&t=1031s\" target=\"_blank\" rel=\"noopener\">\u091c\u0948\u0938\u0947 \u0939\u0940 \u0918\u091f\u093e\u0928\u0947 \u0915\u0940 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e (\u091c\u094b\u0921\u093c \u0915\u0940 \u0909\u0932\u094d\u091f) \u0914\u0930 \u0935\u093f\u092d\u093e\u091c\u0928<\/span><\/strong><\/a> (\u0909\u0924\u094d\u092a\u093e\u0926 \u0915\u0940 \u0909\u0932\u094d\u091f) \u0915\u0940 \u091c\u0930\u0942\u0930\u0924 \u0925\u0940 \u0924\u093e\u0915\u093f \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094b \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915 \u0914\u0930 \u0924\u0930\u094d\u0915\u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u092e\u0947\u0902 \u0935\u093f\u0938\u094d\u0924\u093e\u0930 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0947, \u0920\u0940\u0915 \u0909\u0938\u0940 \u0924\u0930\u0939 \u0938\u0947 \u0918\u093e\u0924\u094b\u0902 \u0915\u0947 \u0938\u093e\u0925 \u092d\u0940 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0918\u093e\u0924 n<\/span> \u0915\u0940 \u0909\u0932\u094d\u091f \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0939\u0948 \u091c\u0921\u093c n<\/span>-esima\u0964<\/p>\n<h3>\u091c\u0921\u093c \u0915\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093e<\/h3>\n<a href=\"https:\/\/www.youtube.com\/watch?v=PfK-pIlyCj4&t=1071s\" target=\"_blank\" rel=\"noopener\">\u092e\u093e\u0928 \u0932\u093f\u091c\u093f\u090f n<\/span> 1 \u0938\u0947 \u0905\u0927\u093f\u0915 \u090f\u0915 \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915 \u0939\u0948<\/span><\/strong><\/a> \u0914\u0930 p,q<\/span> \u0915\u093f\u0938\u0940 \u092d\u0940 \u0924\u0930\u094d\u0915\u0938\u0902\u0916\u094d\u092f\u093e \u0939\u094b\u0924\u0940 \u0939\u0948, \u0939\u092e q<\/span> \u0915\u0940 n<\/span>-esima \u091c\u0921\u093c \u0915\u094b \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0928\u093f\u092f\u092e\u094b\u0902 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f\u092e \u0938\u0947 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<table>\n<tbody>\n<tr style=\"text-align: justify; color: #000000;\">\n<td>16.<\/td>\n<td>q=0 \\rightarrow \\sqrt[n]{q} = 0<\/span><\/td>\n<\/tr>\n<tr style=\"text-align: justify; color: #000000;\">\n<td>17.<\/td>\n<td>q \\gt 0 \\rightarrow \\left[ \\sqrt[n]{q} = p \\leftrightarrow p^n = q \\right]<\/span><\/td>\n<\/tr>\n<tr style=\"text-align: justify; color: #000000;\">\n<td>18.<\/td>\n<td> \\left[ q \\lt 0 \\wedge n {\\;\u0939\u0948\\;\u0935\u093f\u0937\u092e} \\right]\\rightarrow \\left[ \\sqrt[n]{q} = p \\leftrightarrow p^n = q \\right]<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\u0938\u0902\u0915\u094d\u0937\u0947\u092a \u092e\u0947\u0902, q<\/span> \u0915\u0940 n<\/span>-esima \u091c\u0921\u093c \u090f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e p<\/span> \u0939\u094b\u0924\u0940 \u0939\u0948 \u091c\u094b, n<\/span> \u092a\u0930 \u0909\u0920\u093e\u092f\u093e \u091c\u093e\u0924\u0947 \u0939\u0941\u090f, \u0906\u092a\u0915\u094b \u0938\u0902\u0916\u094d\u092f\u093e q<\/span> \u0935\u093e\u092a\u0938 \u0926\u0947\u0924\u0940 \u0939\u0948\u0964 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930, \u091c\u092c n=2<\/span> \u0939\u094b\u0924\u093e \u0939\u0948, \u0939\u092e \\sqrt[2]{q}<\/span> \u0932\u093f\u0916\u0928\u0947 \u0915\u0947 \u092c\u091c\u093e\u092f \u0938\u0930\u0932\u0924\u093e \u0915\u0947 \u0932\u093f\u090f \\sqrt{q}.<\/span> \u0932\u093f\u0916\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<h3>\u0905\u0924\u0930\u094d\u0915\u0938\u0902\u0916\u094d\u092f\u093e \u0915\u0940 \u0909\u0924\u094d\u092a\u0924\u094d\u0924\u093f<\/h3>\n<a href=\"https:\/\/www.youtube.com\/watch?v=PfK-pIlyCj4&t=1216s\" target=\"_blank\" rel=\"noopener\">\u0907\u0938 \u092c\u093f\u0902\u0926\u0941 \u092a\u0930 \u092a\u0939\u0941\u0902\u091a\u0915\u0930 \u0939\u092e \u0938\u094b\u091a\u0924\u0947 \u0939\u0948\u0902<\/span><\/strong><\/a> \u0915\u093f \u0915\u094d\u092f\u093e \\mathbb{Q}<\/span> \u0915\u0947 \u0938\u092d\u0940 \u0924\u0924\u094d\u0935\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f n-\u091c\u0921\u093c \u0938\u0939\u0940 \u0924\u0930\u0940\u0915\u0947 \u0938\u0947 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0939\u0948? \u0938\u091a \u092f\u0939 \u0939\u0948 \u0915\u093f, \u092f\u0926\u094d\u092f\u092a\u093f \u092f\u0939 \u0907\u0924\u0928\u093e \u0938\u094d\u092a\u0937\u094d\u091f \u0928\u0939\u0940\u0902 \u0939\u0948 (\u0924\u0941\u0932\u0928\u093e \u092e\u0947\u0902 \u0918\u091f\u093e\u0928\u093e \u0914\u0930 \u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u0947 \u0938\u093e\u0925), \u0915\u0941\u091b \u0924\u0930\u094d\u0915\u0938\u0902\u0916\u094d\u092f\u093e \u0939\u0948\u0902 \u091c\u093f\u0928\u0915\u093e \u0924\u0930\u094d\u0915\u0938\u0902\u0916\u094d\u092f\u093e \u0928-\u091c\u0921\u093c \u0928\u0939\u0940\u0902 \u0939\u0948\u0964 \u0907\u0938\u0947 \u0926\u0947\u0916\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0940 \u0938\u092e\u0940\u0915\u094d\u0937\u093e \u0915\u0930\u0928\u093e \u0915\u093e\u092b\u0940 \u0939\u0948:<\/p>\n\\sqrt{2}<\/span> \u090f\u0915 \u0924\u0930\u094d\u0915\u0938\u0902\u0916\u094d\u092f\u093e \u0928\u0939\u0940\u0902 \u0939\u0948\u0964<\/strong><\/em><\/p>\n\u092a\u094d\u0930\u092e\u093e\u0923<\/strong><\/p>\n\u0939\u092e \u0907\u0938\u0947 \u0905\u0926\u0930\u094d\u0936 \u0918\u091f\u093e\u0928\u0947 \u0926\u094d\u0935\u093e\u0930\u093e \u092a\u094d\u0930\u092e\u093e\u0923\u093f\u0924 \u0915\u0930\u0947\u0902\u0917\u0947\u0964<\/p>\n\u092e\u093e\u0928 \u0932\u093f\u091c\u093f\u090f \u0915\u093f \\sqrt{2}<\/span> \u090f\u0915 \u0924\u0930\u094d\u0915\u0938\u0902\u0916\u094d\u092f\u093e \u0939\u0948, \u0905\u0930\u094d\u0925\u093e\u0924, p,q\\in\\mathbb{Z}<\/span> \u092e\u094c\u091c\u0942\u0926 \u0939\u0948\u0902, \u091c\u0939\u093e\u0902 q\\neq 0,<\/span> \u0910\u0938\u0947 \u0915\u093f \\sqrt{2}=p\/q,<\/span> \u0914\u0930 \u092f\u0939 \u092d\u0940 \u0938\u0930\u0932 \u092c\u0928\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948\u0964 \u0905\u0917\u0930 \u0939\u092e \u0910\u0938\u093e \u0915\u0930\u0924\u0947 \u0939\u0948\u0902 \u0924\u094b \u0939\u092e \u0915\u0939 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f<\/p>\n2 = \\left(\\sqrt{2} \\right)^2 =\\displaystyle \\frac{p^2}{q^2} = <\/span> \\left(\\displaystyle \\frac{p}{q}\\right)^2<\/span>\n<\/span><\/p>\n\u0932\u0947\u0915\u093f\u0928 \u0907\u0938\u092e\u0947\u0902 \u0935\u093f\u0938\u0902\u0917\u0924\u093f \u0939\u0948 \u0915\u093f p\/q<\/span> \u0938\u0930\u0932 \u0930\u0942\u092a \u092e\u0947\u0902 \u0932\u093f\u0916\u093e \u0917\u092f\u093e \u0925\u093e (\u0905\u092c \u092f\u0939 \u0928\u093f\u0915\u0932\u0924\u093e \u0939\u0948 \u0915\u093f (p\/q)^2<\/span> \u0915\u094b \u0938\u0930\u0932\u0940\u0915\u0943\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 \u0914\u0930 \u0907\u0938\u0915\u093e \u092a\u0930\u093f\u0923\u093e\u092e 2 \u0939\u0948)\u0964 \u091a\u0942\u0902\u0915\u093f \\sqrt{2}<\/span> \u090f\u0915 \u0924\u0930\u094d\u0915\u0938\u0902\u0916\u094d\u092f\u093e \u0939\u094b\u0928\u0947 \u0915\u093e \u092e\u093e\u0928\u0928\u093e \u090f\u0915 \u0935\u093f\u0938\u0902\u0917\u0924\u093f \u092a\u0948\u0926\u093e \u0915\u0930\u0924\u093e \u0939\u0948, \u0907\u0938\u0932\u093f\u090f \u092f\u0939 \u090f\u0915 \u0924\u0930\u094d\u0915\u0938\u0902\u0916\u094d\u092f\u093e \u0928\u0939\u0940\u0902 \u0939\u094b \u0938\u0915\u0924\u093e \u0939\u0948 \u0914\u0930 \u0939\u092e \u0907\u0938\u0947 \u0905\u0924\u0930\u094d\u0915\u0938\u0902\u0916\u094d\u092f\u093e \u0915\u0939\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<h3>\u0924\u0930\u094d\u0915\u0938\u0902\u0916\u094d\u092f\u093e \u092e\u0947\u0902 \u0935\u093f\u0938\u094d\u0924\u093e\u0930<\/h3>\n<a href=\"https:\/\/www.youtube.com\/watch?v=PfK-pIlyCj4&t=1514s\" target=\"_blank\" rel=\"noopener\">\u0907\u0928 \u092a\u0930\u093f\u0923\u093e\u092e\u094b\u0902 \u0915\u094b \u0938\u094d\u092a\u0937\u094d\u091f \u0930\u0942\u092a \u0938\u0947 \u0926\u093f\u0916\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948 \u0915\u093f,<\/span> <\/strong><\/a>\u0928-\u091c\u0921\u093c \u0915\u094b \u0938\u0939\u0940 \u0924\u0930\u0940\u0915\u0947 \u0938\u0947 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092f\u0939 \u091c\u0930\u0942\u0930\u0940 \u0939\u0948 \u0915\u093f \u0924\u0930\u094d\u0915\u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094b \u090f\u0915 \u0928\u0908 \u0938\u092e\u0941\u0926\u093e\u092f \u092e\u0947\u0902 \u092c\u0926\u0932 \u0926\u093f\u092f\u093e \u091c\u093e\u090f, \u092f\u0939 \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u093e \u0938\u092e\u0941\u0926\u093e\u092f \u0939\u0948, \u091c\u093f\u0938\u0947 \u0939\u092e \\mathbb{R}<\/span> \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u091a\u093f\u0939\u094d\u0928\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u091c\u093f\u0938\u092e\u0947\u0902 \u0924\u0930\u094d\u0915\u0938\u0902\u0916\u094d\u092f\u093e \u0914\u0930 \u0905\u0924\u0930\u094d\u0915\u0938\u0902\u0916\u094d\u092f\u093e \u0926\u094b\u0928\u094b\u0902 \u0936\u093e\u092e\u093f\u0932 \u0939\u0948\u0902\u0964<\/p>\n\\mathbb{R}= \\mathbb{Q}\\cup \\mathbb{Q}^*<\/span>\n<a name=\"6\"><\/a><\/p>\n<h2>\u0938\u0902\u0916\u094d\u092f\u093e\u0924\u094d\u092e\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901: \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0940 \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u0936\u0930\u094d\u0924<\/h2>\n<a href=\"https:\/\/www.youtube.com\/watch?v=PfK-pIlyCj4&t=1532s\" target=\"_blank\" rel=\"noopener\">\u0907\u0938 \u092c\u093f\u0902\u0926\u0941 \u092a\u0930 \u0939\u092e\u0947\u0902 \u0926\u094b \u092c\u093e\u0924\u0947\u0902 \u0927\u094d\u092f\u093e\u0928 \u092e\u0947\u0902 \u0930\u0916\u0928\u0940 \u091a\u093e\u0939\u093f\u090f:<\/span><\/strong><\/a> (1) \u091c\u092c n<\/span> \u0938\u092e \u0939\u094b\u0924\u093e \u0939\u0948, n-\u091c\u0921\u093c \u092c\u0939\u0941\u092e\u0941\u0916\u0940 \u092c\u0928 \u091c\u093e\u0924\u093e \u0939\u0948 \u0914\u0930, (2) \u092f\u0926\u093f \u0939\u092e \\sqrt[n]{q}<\/span> \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0928\u0947 \u0915\u093e \u092a\u094d\u0930\u092f\u093e\u0938 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902 \u091c\u0939\u093e\u0901 q\\lt 0,<\/span> \u0924\u094b \u0939\u092e \u0926\u0947\u0916\u0947\u0902\u0917\u0947 \u0915\u093f \u0910\u0938\u093e \u0938\u0902\u0916\u094d\u092f\u093e \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \u0928\u0939\u0940\u0902 \u0939\u094b \u0938\u0915\u0924\u093e\u0964<\/p>\n\u092a\u0939\u0932\u0940 \u092c\u093e\u0924 \u0915\u093e \u0939\u0932 \u0939\u0948 \u092e\u0941\u0916\u094d\u092f \u091c\u0921\u093c<\/strong> \u0915\u094b \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930\u0928\u093e, \u091c\u094b 17 \u0905\u0902\u0915 \u092a\u0930 \u091c\u0921\u093c \u0915\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u092c\u0924\u093e \u0930\u0939\u093e \u0939\u0948, \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0924\u0930\u0940\u0915\u0947 \u0938\u0947 \u0939\u094b\u0924\u093e \u0939\u0948:<\/p>\n<table>\n<tbody>\n<tr style=\"text-align: justify; color: #000000;\">\n<td>17*.<\/td>\n<td>q\\gt 0 \\rightarrow \\left[ 0\\lt p=\\sqrt[n]{q} \\leftrightarrow p^n=q \\right]<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\u0926\u0942\u0938\u0930\u093e \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u0947 \u0938\u092e\u0941\u0926\u093e\u092f \u0915\u094b \u0938\u0902\u0916\u094d\u092f\u093e\u0924\u094d\u092e\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u0947 \u0938\u092e\u0941\u0926\u093e\u092f \\mathbb{C}<\/span> \u092e\u0947\u0902 \u0935\u093f\u0938\u094d\u0924\u093e\u0930\u093f\u0924 \u0915\u0930\u0915\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0932\u0947\u0915\u093f\u0928 \u0907\u0938 \u0928\u093f\u0930\u094d\u092e\u093e\u0923 \u0915\u094b \u092c\u093e\u0926 \u092e\u0947\u0902 \u091b\u094b\u0921\u093c \u0926\u093f\u092f\u093e \u091c\u093e\u090f\u0917\u093e\u0964<\/p>\n<\/html><\/p>\n","protected":false},"excerpt":{"rendered":"\u0938\u0902\u0916\u094d\u092f\u093e \u0938\u092e\u0941\u091a\u094d\u091a\u092f\u094b\u0902 \u0915\u0940 \u092a\u0939\u0932\u0940 \u092a\u0939\u091a\u093e\u0928 – ToposUranos.com \u0938\u0902\u0916\u094d\u092f\u093e \u0938\u092e\u0941\u091a\u094d\u091a\u092f\u094b\u0902 \u0915\u0940 \u092a\u0939\u0932\u0940 \u092a\u0939\u091a\u093e\u0928: \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0947 \u091c\u091f\u093f\u0932 \u0924\u0915 \u0938\u093e\u0930\u093e\u0902\u0936:\u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0939\u092e \u091c\u093e\u0902\u091a\u0947\u0902\u0917\u0947 \u0915\u093f \u0915\u0948\u0938\u0947 \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 \u0905\u0928\u094d\u092f \u0938\u0902\u0916\u094d\u092f\u093e \u0938\u092e\u0941\u091a\u094d\u091a\u092f\u094b\u0902 \u0915\u0947 \u0928\u093f\u0930\u094d\u092e\u093e\u0923 \u0915\u0947 \u0906\u0927\u093e\u0930 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0909\u092a\u092f\u094b\u0917 \u0915\u0940 \u091c\u093e \u0938\u0915\u0924\u0940 \u0939\u0948\u0902 \u0924\u093e\u0915\u093f \u0935\u0947 \u0915\u0941\u091b \u0938\u0902\u091a\u093e\u0932\u0928\u0940\u092f \u0938\u0940\u092e\u093e\u0913\u0902 \u0915\u094b \u092a\u093e\u0930 \u0915\u0930 \u0938\u0915\u0947\u0902\u0964 \u0939\u092e \u092a\u0942\u0930\u094d\u0923 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0938\u0947 \u0936\u0941\u0930\u0942 \u0915\u0930\u0947\u0902\u0917\u0947, […]<\/p>\n","protected":false},"author":1,"featured_media":25038,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":0,"footnotes":""},"categories":[577,593,1039],"tags":[],"class_list":["post-24945","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-577","category-593","category-1039"],"yoast_head":"\n<title>\u0938\u0902\u0916\u094d\u092f\u093e\u0924\u094d\u092e\u0915 \u0938\u092e\u0941\u0926\u093e\u092f: 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