Editing Identity element (section)

==Examples==
{| class="wikitable"
! Set !! Operation !! Identity
|-
| rowspan = "2"| [[Real number]]s, [[complex number]]s|| + ([[addition]]) || [[0 (number)|0]]
|-
| · ([[multiplication]]) || [[1 (number)|1]]
|-
| [[Positive integer]]s || [[Least common multiple]] || 1
|-
| [[Non-negative integer]]s || [[Greatest common divisor]] || 0 (under most definitions of GCD)
|-
| rowspan = "2"| [[Vector (mathematics and physics)|Vectors]] || [[Vector addition]]
| [[Zero vector]]
|-
|[[Scalar multiplication]] || [[1 (number)|1]]
|-
<!-- ||' ''R'''<sup>''n''</sup> || · (multiplication) || [[1 (number)|1]] -->
| {{mvar|m}}-by-{{mvar|n}} [[matrix (mathematics)|matrices]] || [[Matrix addition]]
| [[Zero matrix]]
|-
| {{mvar|n}}-by-{{mvar|n}} square matrices || [[Matrix multiplication]]
| ''I''<sub>''n''</sub> ([[identity matrix]])
|-
| {{mvar|m}}-by-{{mvar|n}} matrices || ○ ([[Hadamard product (matrices)|Hadamard product]])
| {{math|''J''<sub>''m'', ''n''</sub>}} ([[matrix of ones]])
|-
| All [[function (mathematics)|functions]] from a set,&nbsp;{{mvar|M}}, to itself || ∘ ([[function composition]]) || [[Identity function]]
|-
| All [[distribution (mathematics)|distributions]] on a [[group (mathematics)|group]],&nbsp;{{mvar|G}}<!-- a crap refurbished --> || ∗ ([[convolution]]) || {{math|''δ''}} ([[Dirac delta]])
|-
| rowspan = "2" | [[Extended real number]]s || [[Minimum]]/infimum || +∞
|-
|| [[Maximum]]/supremum || −∞
|-
| rowspan = "2" | Subsets of a [[Set (mathematics)|set]]&nbsp;{{mvar|M}} || ∩ ([[set intersection|intersection]]) || {{mvar|M}}
|-
|| ∪ ([[set union|union]]) || ∅ ([[empty set]])
|-
| [[string (computer science)|Strings]], [[tuple|lists]] || [[Concatenation]] || [[Empty string]], empty list
|-
| rowspan = "4" | A [[Boolean algebra (structure)|Boolean algebra]] || <math display="inline">\and</math> ([[logical conjunction|conjuction]]) || <math display="inline">\top</math> ([[Tautology (logic)|truth]])
|-
|| <math display="inline">\leftrightarrow</math> ([[logical biconditional|equivalence]]) || <math display="inline">\top</math> ([[Tautology (logic)|truth]])
|-
||  <math display="inline">\vee</math> ([[Logical disjunction|disjunction]]) || <math display="inline">\bot</math> ([[Contradiction|falsity]])
|-
|| <math display="inline">\nleftrightarrow</math> ([[Exclusive or|nonequivalence]]) || <math display="inline">\bot</math> ([[Contradiction|falsity]])
|-
| [[knot (mathematics)|Knots]] || [[Knot sum]] || [[Unknot]]
|-
| [[Compact surfaces]] || # ([[connected sum]]) || [[sphere|''S''<sup>2</sup>]]
|-
| [[Group (mathematics)|Groups]] || [[Direct product]] || [[Trivial group]]
|-
| Two elements, {{math|{''e'', ''f''} }}
| ∗ defined by<br> {{math|1=''e'' ∗ ''e'' = ''f'' ∗ ''e'' = ''e''}} and <br> {{math|1=''f'' ∗ ''f'' = ''e'' ∗ ''f'' = ''f''}}
| Both {{mvar|e}} and {{mvar|f}} are left identities,<br> but there is no right identity<br> and no two-sided identity
|-
| [[Homogeneous relation]]s on a set ''X'' || [[Relative product]] || [[Identity relation]]
|-
| [[Relational algebra]] || [[Natural join]] (⨝) || The unique relation [[relation of degree zero|degree zero]] and cardinality one
|}