Math

Discrete Math Symbols: Symbol Meaning Usage Example Reads as ∃ There exists ∃ ∃x There exists x ∈ Element of x ∈ S x ∈ {1, 2, 3} x is an element of S ∉ Not an element of x ∉ S x ∉ {1, 2, 3} x is not an element of S ∣ Divides x ∣ y 3 ∣ 9 3 divides 9 Z Integers Z Z+ Set of positive integers ≡ Congruent x ≡ y 0 ≡ 10%5 0 is congruent to 10 mod 5 Full set of symbols generated by CoPilot: Symbol Meaning ∈ Element of ∉ Not an element of ∅ Empty set ⊆ Subset ⊂ Proper subset ⊄ Not a subset ⊇ Superset ⊃ Proper superset ⊅ Not a superset ∪ Union ∩ Intersection ∖ Set difference ∆ Symmetric difference ⊕ Exclusive or ⊖ Not exclusive or ⊗ Cartesian product ⊸ Subset of or equal to ⊃⊸ Proper subset of or equal to ⊻ Disjoint union ⊼ Not disjoint union ⊽ Multiset union ⊾ Multiset intersection ⊿ Multiset difference ⊙ Multiset sum ⊚ Multiset product ⊛ Multiset disjoint union ⊜ Multiset symmetric difference ⊝ Multiset subset ⊞ Multiset superset ⊟ Multiset subset of or equal to ⊠ Multiset superset of or equal to ⊡ Multiset subset of or equal to ⊢ Proves ⊣ Is proved by ⊤ Tautology ⊥ Contradiction ⊦ Entails ⊧ Satisfies ⊨ Models ⊩ Forces ⊪ Is forced by ⊫ Is true under ⊬ Is false under ⊭ Does not entail ⊮ Does not satisfy ⊯ Does not model ⊰ Is consistent with ⊱ Is inconsistent with ⊲ Precedes ⊳ Succeeds ⊴ Is a normal subgroup of ⊵ Contains as normal subgroup ⊶ Is a subgroup of ⊷ Contains as subgroup ⊸ Normal subgroup of or equal to ⊹ Subgroup of or equal to ⊺ Contains as normal subgroup or equal to ⊻ Contains as subgroup or equal to ⊼ Isomorphic to ⊽ Isomorphic with ⊾ Isomorphic to or equal to ⊿ Isomorphic with or equal to ⋀ Logical and ⋁ Logical or ⋂ Generalized intersection ⋃ Generalized union ⋄ Diamond ⋅ Dot operator ⋆ Star operator ⋇ Division times ⋈ Bowtie ⋉ Left normal factor semidirect product ⋊ Right normal factor semidirect product ⋋ Left semidirect product ⋌ Right semidirect product ⋍ Reversed tilde ⋎ Logical or with dot above ⋏ Logical and with dot above ⋐ Double subset ⋑ Double superset ⋒ Double intersection ⋓ Double union ⋔ Pitchfork ⋕ Equal and parallel to ⋖ Less-than with dot ⋗ Greater-than with dot ⋘ Very much less-than ⋙ Very much greater-than ⋚ Less-than equal to or greater-than ⋛ Greater-than equal to or less-than ⋜ Equal to or less-than ⋝ Equal to or greater-than ⋞ Equal to or precedes ⋟ Equal to or succeeds ⋠ Does not precede or equal ⋡ Does not succeed or equal ⋢ Not square image of or equal to ⋣ Not square original of or equal to ⋤ Square image of or not equal to ⋥ Square original of or not equal to ⋦ Less-than but not equivalent to ⋧ Greater-than but not equivalent to ⋨ Precedes but not equivalent to ⋩ Succeeds but not equivalent to ⋪ Not normal subgroup of ⋫ Does not contain as normal subgroup ⋬ Not normal subgroup of or equal to ⋭ Does not contain as normal subgroup or equal ⋮ Vertical ellipsis ⋯ Midline horizontal ellipsis ⋰ Up right diagonal ellipsis ⋱ Down right diagonal ellipsis ⋲ Element of with long horizontal stroke ⋳ Element of with vertical bar at end of horizontal stroke ⋴ Small element of with vertical bar at end of horizontal stroke ⋵ Element of with dot above ⋶ Element of with overbar ⋷ Small element of with overbar ⋸ Element of with underbar ⋹ Element of with two horizontal strokes ⋺ Contains with long horizontal stroke ⋻ Contains with vertical bar at end of horizontal stroke ⋼ Small contains with vertical bar at end of horizontal stroke ⋽ Contains with overbar ⋾ Contains with underbar ⋿ Z notation bag membership ⌀ Diameter sign ⌁ Electric arrow ⌂ House ⌃ Up arrowhead ⌄ Down arrowhead ⌅ Projective ⌆ Perspective ⌇ Wavy line ⌈ Left ceiling ⌉ Right ceiling ⌊ Left floor ⌋ Right floor ⌌ Bottom right crop ⌍ Bottom left crop ⌎ Top right crop ⌏ Top left crop ⌐ Reversed not sign ⌑ Square lozenge ⌒ Arc ⌓ Segment ⌔ Sector ⌕ Telephone recorder ⌖ Position indicator ⌗ Viewdata square ⌘ Place of interest sign ⌙ Turned not sign ⌜ Top left corner

Integer Division Integer division is a division operation that falls under number theory, a branch of math that is concerned with studying the properties of integers. In integer division, both the inputs and the output are integers resulting in being able to find an integer quotient and an integer remainder given two other integers. Divides For 2 integers $x$ and $y$, if there is an integer $k$ such that $y=kx$, then $x$ divides, $y$ is a multiple of $x$, $x$ is a factor/divisor of $y$....