Properties Subtraction

1 properties

1.1 anticommutativity
1.2 non-associativity
1.3 predecessor

properties
anticommutativity

subtraction anti-commutative, meaning if 1 reverses terms in difference left-to-right, result negative of original result. symbolically, if , b 2 numbers, then

a − b = −(b − a).

non-associativity

subtraction non-associative, comes when 1 tries define repeated subtraction. should expression

− b − c

be defined mean (a − b) − c or − (b − c)? these 2 possibilities give different answers. resolve issue, 1 must establish order of operations, different orders giving different results.

predecessor

in context of integers, subtraction of 1 plays special role: integer a, integer (a − 1) largest integer less a, known predecessor of a.