{"id":3113,"date":"2019-06-12T15:13:39","date_gmt":"2019-06-12T15:13:39","guid":{"rendered":"http:\/\/softlect.in\/?p=3113"},"modified":"2020-04-08T20:40:57","modified_gmt":"2020-04-08T20:40:57","slug":"set-theory-symbols","status":"publish","type":"post","link":"http:\/\/softlect.com\/index.php\/set-theory-symbols\/","title":{"rendered":"Set Theory Symbols"},"content":{"rendered":"

Set Theory Symbols<\/h1>\n
\n
\n
Symbol<\/strong><\/div>\n
Meaning \/ definition<\/strong><\/div>\n
Example<\/strong><\/div>\n<\/div>\n
\n
{ }<\/div>\n
a collection of elements<\/div>\n
A = {3,7,9,14},
\nB = {9,14,28}<\/div>\n<\/div>\n
\n
A \u2229 B<\/div>\n
objects that belong to set A and set B<\/div>\n
A \u2229 B = {9,14}<\/div>\n<\/div>\n
\n
A \u222a B<\/div>\n
objects that belong to set A or set B<\/div>\n
A \u222a B = {3,7,9,14,28}<\/div>\n<\/div>\n
\n
A \u2286 B<\/div>\n
subset has fewer elements or equal to the set<\/div>\n
{9,14,28} \u2286 {9,14,28}<\/div>\n<\/div>\n
\n
A \u2282 B<\/div>\n
subset has fewer elements than the set<\/div>\n
{9,14} \u2282 {9,14,28}<\/div>\n<\/div>\n
\n
A \u2284 B<\/div>\n
left set not a subset of right set<\/div>\n
{9,66} \u2284 {9,14,28}<\/div>\n<\/div>\n
\n
A \u2287 B<\/div>\n
set A has more elements or equal to the set B<\/div>\n
{9,14,28} \u2287 {9,14,28}<\/div>\n<\/div>\n
\n
A \u2283 B<\/div>\n
set A has more elements than set B<\/div>\n
{9,14,28} \u2283 {9,14}<\/div>\n<\/div>\n
\n
A \u2285 B<\/div>\n
set A is not a superset of set B<\/div>\n
{9,14,28} \u2285 {9,66}<\/div>\n<\/div>\n
\n
2power set<\/sup><\/div>\n
all subsets of A<\/div>\n
<\/div>\n<\/div>\n
\n
\"\\mathcal{P}(A)\"<\/div>\n
all subsets of A<\/div>\n
<\/div>\n<\/div>\n
\n
A = B<\/div>\n
both sets have the same members<\/div>\n
A={3,9,14},
\nB={3,9,14},
\nA=B<\/div>\n<\/div>\n
\n
Ac<\/sup><\/div>\n
all the objects that do not belong to set A<\/div>\n
<\/div>\n<\/div>\n
\n
A \\ B<\/div>\n
objects that belong to A and not to B<\/div>\n
A = {3,9,14},
\nB = {1,2,3},
\nA-B = {9,14}<\/div>\n<\/div>\n
\n
A – B<\/div>\n
objects that belong to A and not to B<\/div>\n
A = {3,9,14},
\nB = {1,2,3},
\nA-B = {9,14}<\/div>\n<\/div>\n
\n
A \u2206 B<\/div>\n
objects that belong to A or B but not to their intersection<\/div>\n
A = {3,9,14},
\nB = {1,2,3},
\nA \u2206 B = {1,2,9,14}<\/div>\n<\/div>\n
\n
A \u2296 B<\/div>\n
objects that belong to A or B but not to their intersection<\/div>\n
A = {3,9,14},
\nB = {1,2,3},
\nA \u2296 B = {1,2,9,14}<\/div>\n<\/div>\n
\n
a<\/em>\u2208A<\/div>\n
set membership<\/div>\n
A={3,9,14}, 3 \u2208 A<\/div>\n<\/div>\n
\n
x<\/em>\u2209A<\/div>\n
no set membership<\/div>\n
A={3,9,14}, 1 \u2209 A<\/div>\n<\/div>\n
\n
(a<\/em>,b<\/em>)<\/div>\n
collection of 2 elements<\/div>\n
<\/div>\n<\/div>\n
\n
A\u00d7B<\/div>\n
set of all ordered pairs from A and B<\/div>\n
<\/div>\n<\/div>\n
\n
|A|<\/div>\n
the number of elements of set A<\/div>\n
A={3,9,14}, |A|=3<\/div>\n<\/div>\n
\n
#A<\/div>\n
the number of elements of set A<\/div>\n
A={3,9,14}, #A=3<\/div>\n<\/div>\n
\n
\"\"<\/div>\n
infinite cardinality of natural numbers set<\/div>\n
<\/div>\n<\/div>\n
\n
\"\"<\/div>\n
cardinality of countable ordinal numbers set<\/div>\n
<\/div>\n<\/div>\n
\n
\u00d8<\/div>\n
\u00d8 = { }<\/div>\n
C = {\u00d8}<\/div>\n<\/div>\n
\n
\"\\mathbb{U}\"<\/div>\n
set of all possible values<\/div>\n
<\/div>\n<\/div>\n
\n
\"\\mathbb{N}\"0<\/sub><\/div>\n
\"\\mathbb{N}\"0<\/sub> = {0,1,2,3,4,…}<\/div>\n
0 \u2208 \"\\mathbb{N}\"0<\/sub><\/div>\n<\/div>\n
\n
\"\\mathbb{N}\"1<\/sub><\/div>\n
\"\\mathbb{N}\"1<\/sub> = {1,2,3,4,5,…}<\/div>\n
6 \u2208 \"\\mathbb{N}\"1<\/sub><\/div>\n<\/div>\n
\n
\"\\mathbb{Z}\"<\/div>\n
\"\\mathbb{Z}\" = {…-3,-2,-1,0,1,2,3,…}<\/div>\n
-6 \u2208 \"\\mathbb{Z}\"<\/div>\n<\/div>\n
\n
\"\\mathbb{Q}\"<\/div>\n
\"\\mathbb{Q}\" = {x <\/em>| x<\/em>=a<\/em>\/b<\/em>, a<\/em>,b<\/em>\u2208\"\\mathbb{Z}\"}<\/div>\n
2\/6 \u2208 \"\\mathbb{Q}\"<\/div>\n<\/div>\n
\n
\"\\mathbb{R}\"<\/div>\n
\"\\mathbb{R}\" = {x<\/em> | -\u221e < x <\/em><\u221e}<\/div>\n
6.343434 \u2208 \"\\mathbb{R}\"<\/div>\n<\/div>\n
\n
\"\\mathbb{C}\"<\/div>\n
\"\\mathbb{C}\" = {z <\/em>| z=a<\/em>+bi<\/em>, -\u221e<a<\/em><\u221e, -\u221e<b<\/em><\u221e}<\/div>\n
6+2i<\/em> \u2208 \"\\mathbb{C}\"<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Set Theory Symbols Symbol Meaning \/ definition Example { } a collection of elements A = {3,7,9,14}, B = {9,14,28} A \u2229 B objects that belong to set A and… <\/p>\n","protected":false},"author":1,"featured_media":3130,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[34],"tags":[],"aioseo_notices":[],"amp_enabled":true,"_links":{"self":[{"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/posts\/3113"}],"collection":[{"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/comments?post=3113"}],"version-history":[{"count":4,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/posts\/3113\/revisions"}],"predecessor-version":[{"id":3688,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/posts\/3113\/revisions\/3688"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/media\/3130"}],"wp:attachment":[{"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/media?parent=3113"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/categories?post=3113"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/softlect.com\/index.php\/wp-json\/wp\/v2\/tags?post=3113"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}