{"id":2403,"date":"2020-10-22T21:31:33","date_gmt":"2020-10-23T00:31:33","guid":{"rendered":"https:\/\/www.blogs.unicamp.br\/zero\/?p=2403"},"modified":"2022-05-23T17:40:19","modified_gmt":"2022-05-23T20:40:19","slug":"youre-weak-lemma-you-lack-importance","status":"publish","type":"post","link":"https:\/\/www.blogs.unicamp.br\/zero\/2403\/","title":{"rendered":"You’re weak lemma, you lack importance!"},"content":{"rendered":"\n

In mathematics we often hear that something is a Corollary<\/strong>, something else is a Lemma<\/strong>, that is a Proposition<\/strong>, there is a Theorem<\/strong> \u2026 We also have terms such as Rules<\/strong>, Laws<\/strong>, Properties<\/strong>, but these seem to have their general meanings for clearer results, for example: Sum of Derivatives Rule<\/strong> \u2026 is a result related to the sum operation with derivatives; Law of Sines<\/strong> \u2026 is a result that determines for any triangle, the relation of the sine of an angle is always proportional to the measure of the opposite side to that angle; Distributive property of multiplication<\/strong> \u2026 is a result that guarantees a(b + c) = ab + cd.<\/p>\n\n\n\n

So, let’s focus on the 4 terms with the most obscure meanings (Corollary<\/strong>, Lemma<\/strong>, Proposition<\/strong>, Theorem<\/strong>), what are these names anyway? Let’s start by looking at the dictionary.<\/p>\n\n\n\n

Corollary<\/strong>: proposition that derives, in a deductive chain, from a preceding assertion, producing an increase of knowledge through the explanation of aspects that, in the previous statement, remained latent or obscure;<\/p>\n\n\n\n

Lemma<\/strong>: preliminary proposal whose prior demonstration is necessary to demonstrate the main thesis that is intended to be established;<\/p>\n\n\n\n

Proposition<\/strong>: statement translatable into mathematical symbols, subject to multiple truth values \u200b\u200b(true, false, indeterminate, etc.) and reducible to two basic elements (the subject and the predicate);<\/p>\n\n\n\n

Theorem<\/strong>: proposition that can be demonstrated through a logical process.<\/p>\n\n\n\n

You may have noticed what they look like. And in fact there is a reason for that, these terms are all Tautologies<\/strong>. We will consult in the dictionary what a Tautology<\/strong> is.<\/p>\n\n\n\n

Tautology<\/strong>: analytical proposition that always remains true, since the attribute is a repetition of the subject.<\/p>\n\n\n\n

In fact, Corollaries<\/strong>, Lemmas<\/strong>, Propositions<\/strong> and Theorems<\/strong>, are all Tautologies<\/strong>, that is, sentences whose veracity has been proved in a deductive way. Their differences revolve more around the uses, in this case, the most important results are called Theorems<\/strong>. The less important results, but necessary beforehand to prove a theorem, are called Lemmas<\/strong>. The results obtained directly from a previous result (either a Lemma<\/strong> or a Theorem<\/strong>), are called Corollaries<\/strong>. And Propositions<\/strong> are generally used to describe results of little importance, which are not direct consequences and are not used to demonstrate a Theorem<\/strong>. I drafted these ideas to facilitate understanding.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

However, this is more a convention than a rule. To say that a result is a Theorem<\/strong>, Corollary<\/strong>, Proposition<\/strong>, Lemma<\/strong>, Rule<\/strong>, Property<\/strong>, Law<\/strong> \u2026 is to say that this result was demonstrated in a deductive way based on an adopted axiomatic system. In terms of tautologies<\/strong>, they are all the same. But in terms of social prestige, theorems<\/strong> are superior! And so I justify the cover image of this post, which makes reference to a meme about the anime Naruto, in which Itachi, Sasuke’s brother, defeats and scolds him, saying that he is weak because he lacks hatred! In this case, a theorem<\/strong> is rebuking a lemma<\/strong>, saying that it is weak, because it lacks importance \u2026<\/p>\n\n\n\n

Image adapted of Please Don\u2019t sell My Artwork AS IS<\/a> from Pixabay<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

In mathematics we often hear that something is a Corollary, something else is a Lemma, that is a Proposition, there<\/p>\n","protected":false},"author":434,"featured_media":2404,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"colormag_page_container_layout":"default_layout","colormag_page_sidebar_layout":"default_layout","_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-2403","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\/2403","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=2403"}],"version-history":[{"count":2,"href":"https:\/\/www.blogs.unicamp.br\/zero\/wp-json\/wp\/v2\/posts\/2403\/revisions"}],"predecessor-version":[{"id":2408,"href":"https:\/\/www.blogs.unicamp.br\/zero\/wp-json\/wp\/v2\/posts\/2403\/revisions\/2408"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.blogs.unicamp.br\/zero\/wp-json\/wp\/v2\/media\/2404"}],"wp:attachment":[{"href":"https:\/\/www.blogs.unicamp.br\/zero\/wp-json\/wp\/v2\/media?parent=2403"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.blogs.unicamp.br\/zero\/wp-json\/wp\/v2\/categories?post=2403"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.blogs.unicamp.br\/zero\/wp-json\/wp\/v2\/tags?post=2403"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}