What is identity property of addiction?

Answer 1

The identity property of addition is a property of a set S with some binary function + (referred to as addition) defined over SxS so that whenever a and b are elements of S, +(a,b) = c is also an element of S. It is common to write +(a,b) as a + b and the definition of such a function creates an algebraic structure over S, usually only as part of some larger structure, ie., a group or a field.

The identity property of addition is an axiom that serves to further restrict the type of function + is allowed to be. Specifically, it states that there exists an element of S (for example e), such that for each element a of S, a + e = a. e is usually written as 0, since it behaves like 0 in standard addition over real numbers (0 is the additive identity in the field of real numbers).