Subtraction
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The subtraction is usually considered as one of the four fundamental arithmetic operations, even though we can express subtraction in terms of addition.
In ℕ, with ∀xy ∈ ℕ, we only have addition and multiplication defined as usual, and we have special variants of subtraction and division. Namely, instead of the genral division which requires a field, and we only have a group, we can define saturated subtraction as x ∸ y = z for xyz ∈ ℕ ∧ x >= y
; otherwise, in case x < y
, we can set a constant return value to 0:
x - y = x + (-y)