Identity element

In mathematics, the identity element (or neutral element) of a set is a special element of that set. It is special because if it is combined with another element of that set, it does not change the other element.

With addition, the identity element is 0, because adding 0 to some number does not change the number. With multiplication, it is 1. In a group (an algebraic structure in mathematics), the identity element is sometimes denoted by the symbol .

Further Examples
setoperationidentityreal numbers+ (addition)0real numbers• (multiplication)1real numbersab (exponentiation)1 (right identity only)m-by-n matrices + (addition)zero matrixn-by-n square matrices • (multiplication)identity matrixall functions from a set M to itself∘ (function composition)identity mapcharacter strings, lists concatenation  empty string, empty listextended real numbers  minimum/infimum  +∞extended real numbers  maximum/supremum  -∞subsets of a set M  ∩ (intersection)  Msets  ∪ (union)  {} (empty set)boolean logic  ∧ (logical and)  ⊤ (truth)boolean logic  ∨ (logical or)  ⊥ (falsity)only two elements {e, f}* defined by e * e = f * e = e and  f * f = e * f = fboth e and f are left identities, but there is no right or two-sided identity

 Related pages 

 Identity (mathematics)
 Null vector
 One
 Zero

 References 

Category:Algebra
Category:Abstract algebra