{"id":2288,"date":"2020-07-27T11:30:34","date_gmt":"2020-07-27T14:30:34","guid":{"rendered":"https:\/\/www.blogs.unicamp.br\/zero\/?p=2288"},"modified":"2022-05-23T17:38:27","modified_gmt":"2022-05-23T20:38:27","slug":"who-passes-x-dividing-without-specifying-a-non-null-domain","status":"publish","type":"post","link":"https:\/\/www.blogs.unicamp.br\/zero\/2288\/","title":{"rendered":"Who passes x dividing without specifying a non-null domain"},"content":{"rendered":"\n<p>In those days (end of July \/ 2020) several memes of people circulate doing supposedly absurd things and being represented as gigantic and monstrous creatures, while a simple human in the scene would be the devil near these people. I find these comparisons very funny, but there was one that generated a little &#8220;discussion&#8221; among my friends.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img fetchpriority=\"high\" decoding=\"async\" width=\"622\" height=\"803\" src=\"https:\/\/www.blogs.unicamp.br\/zero\/wp-content\/uploads\/sites\/187\/2020\/07\/meme-ingles.jpg\" alt=\"\" class=\"wp-image-2290\" srcset=\"https:\/\/www.blogs.unicamp.br\/zero\/wp-content\/uploads\/sites\/187\/2020\/07\/meme-ingles.jpg 622w, https:\/\/www.blogs.unicamp.br\/zero\/wp-content\/uploads\/sites\/187\/2020\/07\/meme-ingles-232x300.jpg 232w\" sizes=\"(max-width: 622px) 100vw, 622px\" \/><figcaption>Original image adapted from http:\/\/www.guiadosquadrinhos.com\/personagem\/cthulhu-\/40557<\/figcaption><\/figure><\/div>\n\n\n\n<p>The point of this meme is that in mathematics we always need to specify the domain of a division as being non-zero. That is, for a variable in the denominator, guaranteeing the values \u200b\u200bthat bring the denominator to 0, should not be considered. This is basically &#8220;specifying a domain&#8221;. For example, to say that a prime number is any number that can only be divisible by 1 and by itself, that would be wrong if we do not specify the domain of that property. If it is in the rational \/ real \/ irrational, then there are no prime numbers, since any number of these 3 sets can be divided by infinite numbers. However, if we specify the domain in Integers, we are also saying that there are no prime numbers, since any number other than 0 can be divided by -1 and its additive opposite. More generally, this definition of prime numbers applies only to the domain of natural numbers.<\/p>\n\n\n\n<p>Note in the paragraph above, that when I mentioned that any integer number can be divided by its additive opposite, I remembered to remove 0. I did this because the additive opposite of 0 is 0 itself, and the division by 0 is not defined. Care is taken to justify the consistency of this meme.<\/p>\n\n\n\n<p>Although this seems a little trivial, or even obvious, I bet you&#8217;ve seen a &#8220;trick&#8221; showing how to get that 2 = 1. If not, let&#8217;s see now:<\/p>\n\n\n\n<p>Let a = b;<br>a\u00b2 = b.a;<br>a\u00b2 &#8211; b\u00b2 = b.a &#8211; b\u00b2;<br>(a + b). (a-b) = b (a-b);<br>we divide both sides by (a-b);<br>(a + b) = b;<br>Being a + b = b, like a = b, we have:<br>(a + a) = a;<br>2a = a;<br>we divide both sides by a;<br>2 = 1.<\/p>\n\n\n\n<p>See how cool, we arrived at 2 = 1, but why? The answer is simple, because we don&#8217;t specify a non-null domain. This happened when we divided both sides by (a-b), since being a = b, a-b = 0, right at this stage we divide by 0, which is an undefined operation. This allows us to arrive at any result (literally), since dividing by 0 would be absurd, and there is no point in proceeding after absurdity, since we can get what we want from it.<\/p>\n\n\n\n<p>I hope I made clear the explanation of this meme, because there is malice in the hearts of those who spend x sharing without specifying a non-null domain, which even the devil is frightened by these people.<\/p>\n\n\n\n<p>Just out of curiosity, the relationship of mathematics to &#8220;diabolical&#8221; themes is not at all unusual. The philosopher Saint Augustine (AD 354 &#8211; 430) already warns that \u201cThe good Christian must remain alert against mathematicians and all those who make empty prophecies. There is a danger that mathematicians have made an alliance with the devil to obscure the spirit and confine man to the bonds of Hell. \u201d<\/p>\n\n\n\n<p>There is also a very cool book called &#8220;The Devil of Numbers&#8221; by author Hans Magnus Enzensberger. The story takes place around a boy named Robert who is constantly haunted by nightmares involving incomprehensible math in which he is always wrong, until he starts having dreams about a demon named Teplotaxl, who does all sorts of witchcraft with numbers and it changes the way you see math. It is a simple and very pleasant reading, even my mother who has a certain aversion to mathematics read this book and liked it a lot.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In those days (end of July \/ 2020) several memes of people circulate doing supposedly absurd things and being represented<\/p>\n","protected":false},"author":434,"featured_media":2292,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"editor_plus_copied_stylings":"{}","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"pgc_sgb_lightbox_settings":"","_vp_format_video_url":"","_vp_image_focal_point":[],"footnotes":""},"categories":[1213],"tags":[],"class_list":["post-2288","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-v-4-ed-2"],"_links":{"self":[{"href":"https:\/\/www.blogs.unicamp.br\/zero\/wp-json\/wp\/v2\/posts\/2288","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.blogs.unicamp.br\/zero\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.blogs.unicamp.br\/zero\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.blogs.unicamp.br\/zero\/wp-json\/wp\/v2\/users\/434"}],"replies":[{"embeddable":true,"href":"https:\/\/www.blogs.unicamp.br\/zero\/wp-json\/wp\/v2\/comments?post=2288"}],"version-history":[{"count":1,"href":"https:\/\/www.blogs.unicamp.br\/zero\/wp-json\/wp\/v2\/posts\/2288\/revisions"}],"predecessor-version":[{"id":2291,"href":"https:\/\/www.blogs.unicamp.br\/zero\/wp-json\/wp\/v2\/posts\/2288\/revisions\/2291"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.blogs.unicamp.br\/zero\/wp-json\/wp\/v2\/media\/2292"}],"wp:attachment":[{"href":"https:\/\/www.blogs.unicamp.br\/zero\/wp-json\/wp\/v2\/media?parent=2288"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.blogs.unicamp.br\/zero\/wp-json\/wp\/v2\/categories?post=2288"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.blogs.unicamp.br\/zero\/wp-json\/wp\/v2\/tags?post=2288"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}