{"id":41996,"date":"2025-03-10T12:03:16","date_gmt":"2025-03-10T12:03:16","guid":{"rendered":"https:\/\/idea.membrane.com\/songwriter\/?p=41996"},"modified":"2025-03-10T12:03:16","modified_gmt":"2025-03-10T12:03:16","slug":"equivalence","status":"publish","type":"post","link":"https:\/\/kingarthur.com\/songwriter\/2025\/03\/10\/equivalence\/","title":{"rendered":"Equivalence"},"content":{"rendered":"<p><a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/XI\/Equivalence-I.mp3\">Equivalence-I.mp3<\/a><br \/>\n<a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/XI\/Equivalence-I.mp4\">Equivalence-I.mp4<\/a><br \/>\n<a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/XI\/Equivalence-Unplugged-Underground-XVI.mp3\">Equivalence-Unplugged-Underground-XVI.mp3<\/a><br \/>\n<a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/XI\/Equivalence-Unplugged-Underground-XVI.mp4\">Equivalence-Unplugged-Underground-XVI.mp4<\/a><br \/>\n<a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/XI\/Equivalence-intro.mp3\">Equivalence-intro.mp3<\/a><\/p>\n<p>[Intro]<br \/>\n(I meant)<br \/>\nReflexivity<br \/>\n(Symmetry)<br \/>\nTransitivity<br \/>\n(Equivalent)<\/p>\n<p>[Verse 1]<br \/>\nIf by the chance<br \/>\nThe equivalence<br \/>\nHas relevance<br \/>\nTo our circumstance<\/p>\n<p>[Bridge]<br \/>\n(I meant)<br \/>\nReflexivity<br \/>\n(Symmetry)<br \/>\nTransitivity<br \/>\n(Equivalent)<\/p>\n<p>[Chorus]<br \/>\nWhen true is true<br \/>\n(The same truth value)<br \/>\nThe influence<br \/>\n(Of congruence)<\/p>\n<p>[Verse 2]<br \/>\nLove and romance<br \/>\nIs there equivalence<br \/>\nIs there a debate<br \/>\nWith evil and hate<\/p>\n<p>[Bridge]<br \/>\n(I meant)<br \/>\nReflexivity<br \/>\n(Symmetry)<br \/>\nTransitivity<br \/>\n(Equivalent)<\/p>\n<p>[Chorus]<br \/>\nWhen true is true<br \/>\n(The same truth value)<br \/>\nThe influence<br \/>\n(Of congruence)<\/p>\n<p>[Outro]<br \/>\n(I meant)<br \/>\nReflexivity<br \/>\n(Symmetry)<br \/>\nTransitivity<br \/>\n(Equivalent)<\/p>\n<p>A SCIENCE NOTE<\/p>\n<h3 data-start=\"0\" data-end=\"52\"><strong data-start=\"4\" data-end=\"50\">Meaning of Equivalence in Math and Science<\/strong><\/h3>\n<p data-start=\"54\" data-end=\"78\"><strong data-start=\"54\" data-end=\"76\">1. In Mathematics:<\/strong><\/p>\n<ul data-start=\"79\" data-end=\"513\">\n<li data-start=\"79\" data-end=\"232\"><strong data-start=\"81\" data-end=\"96\">Equivalence<\/strong> refers to a relationship between two objects that are considered equal in some specific way, even if they are not strictly identical.<\/li>\n<li data-start=\"233\" data-end=\"431\">It is often defined through an <strong data-start=\"266\" data-end=\"290\">equivalence relation<\/strong>, which must satisfy <strong data-start=\"311\" data-end=\"326\">reflexivity<\/strong>, <strong data-start=\"328\" data-end=\"340\">symmetry<\/strong>, and <strong data-start=\"346\" data-end=\"362\">transitivity<\/strong> (e.g., congruence of geometric figures, modular arithmetic, etc.).<\/li>\n<li data-start=\"432\" data-end=\"513\">In <strong data-start=\"437\" data-end=\"446\">logic<\/strong>, equivalence (\u21d4) means two statements have the same truth value.<\/li>\n<\/ul>\n<p data-start=\"515\" data-end=\"535\"><strong data-start=\"515\" data-end=\"533\">2. In Science:<\/strong><\/p>\n<ul data-start=\"536\" data-end=\"882\">\n<li data-start=\"536\" data-end=\"722\"><strong data-start=\"538\" data-end=\"550\">Physics:<\/strong> Equivalence often refers to fundamental principles like the <strong data-start=\"611\" data-end=\"636\">Equivalence Principle<\/strong> in General Relativity, which states that gravitational and inertial mass are equal.<\/li>\n<li data-start=\"723\" data-end=\"882\"><strong data-start=\"725\" data-end=\"739\">Chemistry:<\/strong> Equivalence can describe <strong data-start=\"765\" data-end=\"786\">equivalent weight<\/strong>, meaning the amount of a substance that reacts with or replaces a standard amount of another.<\/li>\n<\/ul>\n<h3 data-start=\"884\" data-end=\"916\"><strong data-start=\"888\" data-end=\"914\">Symbol for Equivalence<\/strong><\/h3>\n<ul data-start=\"917\" data-end=\"1258\">\n<li data-start=\"917\" data-end=\"1049\"><strong data-start=\"919\" data-end=\"924\">\u2261<\/strong> (Triple bar) \u2192 Used in logic and mathematics to denote strict equivalence (e.g., identity relations, logical equivalence).<\/li>\n<li data-start=\"1050\" data-end=\"1112\"><strong data-start=\"1052\" data-end=\"1057\">\u223c<\/strong> or <strong data-start=\"1061\" data-end=\"1066\">\u2248<\/strong> \u2192 Used to indicate approximate equivalence.<\/li>\n<li data-start=\"1113\" data-end=\"1180\"><strong data-start=\"1115\" data-end=\"1120\">\u2245<\/strong> \u2192 Used for geometric congruence or structural similarity.<\/li>\n<li data-start=\"1181\" data-end=\"1258\"><strong data-start=\"1183\" data-end=\"1188\">\u21d4<\/strong> \u2192 Used in logic to indicate &#8220;if and only if&#8221; (logical equivalence).<\/li>\n<\/ul>\n<h3>From the album &#8220;<a href=\"\/songwriter\/tag\/equals\/\">Equals<\/a>&#8220;<\/h3>\n","protected":false},"excerpt":{"rendered":"<p>Equivalence-I.mp3 Equivalence-I.mp4 Equivalence-Unplugged-Underground-XVI.mp3 Equivalence-Unplugged-Underground-XVI.mp4 Equivalence-intro.mp3 [Intro] (I meant) Reflexivity (Symmetry) Transitivity (Equivalent) [Verse 1] If by the chance The equivalence Has relevance To our circumstance [Bridge] (I meant) Reflexivity (Symmetry) Transitivity (Equivalent) [Chorus] When true is true (The same truth value) The influence (Of congruence) [Verse 2] Love and romance Is there equivalence Is there [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","footnotes":""},"categories":[3,9,14],"tags":[4107],"class_list":["post-41996","post","type-post","status-publish","format-standard","hentry","category-4d-music","category-daniel","category-lyrics","tag-equals"],"_links":{"self":[{"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/posts\/41996","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/comments?post=41996"}],"version-history":[{"count":4,"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/posts\/41996\/revisions"}],"predecessor-version":[{"id":42018,"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/posts\/41996\/revisions\/42018"}],"wp:attachment":[{"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/media?parent=41996"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/categories?post=41996"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/tags?post=41996"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}