Subtraction -

Subtraction is a binary operation. It should not be confused with the negative sign. For natural numbers the the half minus operator is used which does not go below 0.

Definition

Subtraction is defined using the negative sign as (= (- a b) (+ a (-n b))) /edit/peano_new/arithmetic/common/negative.gh/df-minus.

Properties

• Cancellation: (= (- a a) (0)) /edit/peano_new/arithmetic/common/negative.gh/minuscan
• Identity: (= (- a (0)) a) /edit/peano_new/arithmetic/common/negative.gh/minusid

Fraction Examples

• (= (- (2) (/ (1) (3))) (/ (5) (3))) /edit/peano_new/arithmetic/common/calculations/decimal.gh/subtractFractions1
• (= (- (/ (+ (10) (7)) (+ (* (2) (10)) (3))) (/ (7) (+ (10) (8)))) (/ (+ (* (10) (10)) (+ (* (4) (10)) (5))) (+ (* (4) (* (10) (10))) (+ (10) (4))))) /edit/peano_new/arithmetic/common/calculations/decimal.gh/subtractFractions2

Arithmetic Overview