{"id":303,"date":"2013-12-06T10:39:08","date_gmt":"2013-12-06T15:39:08","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/jal\/?page_id=303"},"modified":"2026-03-19T08:10:39","modified_gmt":"2026-03-19T12:10:39","slug":"symbols","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/jal\/courses\/mhf3202\/symbols\/","title":{"rendered":"Symbols"},"content":{"rendered":"\r\n<section class=\"fullwidth-text-block\">\r\n\t<div class=\"container px-0 pt-5\">\r\n\t\t<div class=\"row align-items-start\">\r\n\t\t\t<div class=\"col-12\">\r\n\t\t\t\t\n<h1 class=\"wp-block-heading\">Symbols<\/h1>\n\n\n\n<ul class=\"wp-block-list\"><li>Quantifiers:\n<ul>\n<li>Universal quantifier: \u2200, \/\\: for every, for all<\/li>\n<li>Existential quantifier: \u018e, \\\/: there exists a &#8230; such that, there is some &#8230; such that<\/li>\n<li>Example: (\u2200 y)(\u018e x)[x &gt; y] is symbolic for &#8220;for all y there is some x with x &gt; y&#8221;.<\/li>\n<\/ul>\n<\/li><li>Logical connectives:\n<ul>\n<li>Negation: \u00ac, ~ : not<\/li>\n<li>Conjunction: \u2227, &amp;: and<\/li>\n<li>Disjunction: \u2228, v: or<\/li>\n<li>Implication: \u2192, &#8211;&gt;: implies, if &#8230; , then &#8230; .<\/li>\n<li>Biconditional: &#x2194;, : if and only if<\/li>\n<li>Logical equivalence: \u2261<\/li>\n<\/ul>\n<\/li><\/ul>\n\n\n\n<ul class=\"wp-block-list\"><li>Set theoretic symbols\n<ul>\n<li>Relations\n<ul>\n<li>Membership relation:\n<ul>\n<li>\u2208: is an element of<\/li>\n<li>\u2209: is not an element of<\/li>\n<li>\u220b: has as a member the element<\/li>\n<\/ul>\n<\/li><li>Subset relation: \u2286, \u2282<\/li>\n<li>Superset relation: \u2287, \u2283<\/li>\n<li>Not a subset of relation: \u2284, \u2288<\/li>\n<li>Order relation: \u2264, \u2265 <\/li>\n<\/ul>\n<\/li><li>Operations:\n<ul>\n<li>Union: \u222a, \u22c3<\/li>\n<li>Intersection: \u2229, \u22c2<\/li>\n<li>Set difference: \u2212, \\<\/li>\n<li>Cartesian product: \u00d7<\/li>\n<li>Power set (Weierstrass p): \u2118 or \u2119<\/li>\n<\/ul>\n<\/li><li>Special sets\n<ul>\n<li>The emptyset: \u2205, {}<\/li>\n<li>Set of real numbers: \u211c or \u211d<\/li>\n<li>Set of rational numbers: \u211a = { m\/n | m, n \u2208 \u2124 and n&gt;0 }<\/li>\n<li>Set of natural numbers: \u2115 = { 0, 1, 2, &#8230; }<\/li>\n<li>Set of positive integers: \u2124<sup>+<\/sup> = { 1, 2, 3, &#8230; }<\/li>\n<li>Set of integers: \u2124 = { &#8230; , -3, -2, -1, 0, 1, 2, 3, &#8230; }<\/li>\n<li>Interval notation: (-\u221e,0], [0,1), (1,+\u221e).<\/li>\n<\/ul>\n<\/li><li>Set bracket notation: { x | property P(x) } is symbolic for &#8220;the set of all x such that property P(x) holds&#8221;.<\/li>\n<\/ul>\n<\/li><li>Other mathematical symbols\n<ul>\n<li>Summation: \u2211<\/li>\n<li>Product: \u220f<\/li>\n<li>Cardinals: \u2135<sub>0<\/sub>, \u2135<sub>1<\/sub>, . . . , \u2135<sub>n<\/sub>,<br>\n\u2135<sub>\u03c9<\/sub><\/li>\n<li>Families of sets: \u212c, \u2131, \u210b, \u2112, \u2133, \u211b, \\(\\mathcal{A}, \\mathcal{B}, \\mathcal{C}, \\mathcal{D}, \\mathcal{E}, \\mathcal{F}, \\mathcal{G}, \\mathcal{H}, \\mathcal{I}, \\mathcal{J}, \\mathcal{K}, \\mathcal{L}, \\mathcal{P}, \\mathcal{Q}, \\mathcal{R}, \\mathcal{S},\\mathcal{T}\\) <\/li><\/ul>\n<\/li><\/ul>\n\n\n\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t<\/div>\r\n<\/section>\r\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":145,"featured_media":0,"parent":269,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-303","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/jal\/wp-json\/wp\/v2\/pages\/303","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/jal\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/jal\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/jal\/wp-json\/wp\/v2\/users\/145"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/jal\/wp-json\/wp\/v2\/comments?post=303"}],"version-history":[{"count":10,"href":"https:\/\/people.clas.ufl.edu\/jal\/wp-json\/wp\/v2\/pages\/303\/revisions"}],"predecessor-version":[{"id":1395,"href":"https:\/\/people.clas.ufl.edu\/jal\/wp-json\/wp\/v2\/pages\/303\/revisions\/1395"}],"up":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/jal\/wp-json\/wp\/v2\/pages\/269"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/jal\/wp-json\/wp\/v2\/media?parent=303"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}