Define integer? write and learn properties of integers on addition?
Answers
Integer, whole-valued positive or negative number or 0. ... The integers are generated from the set of counting numbers 1, 2, 3,… and the operation of subtraction. When a counting number is subtracted from itself, the result is zero; for example, 4 − 4 = 0.
There are four mathematical properties which involve addition. The properties are the commutative, associative, additive identity and distributive properties.
Commutative property: When two numbers are added, the sum is the same regardless of the order of the addends. For example 4 + 2 = 2 + 4
Associative Property: When three or more numbers are added, the sum is the same regardless of the grouping of the addends. For example (2 + 3) + 4 = 2 + (3 + 4)
Additive Identity Property: The sum of any number and zero is the original number. For example 5 + 0 = 5.
Distributive property: The sum of two numbers times a third number is equal to the sum of each addend times the third number. For example 4 * (6 + 3) = 4*6 + 4*3
Answer:
Integer Property Addition Subtraction
Associative Property x + (y + z) = (x + y) +z (x – y) – z ≠ x – (y – z)
Identity Property x + 0 = x =0 + x x – 0 = x ≠ 0 – x
Closure Property x + y ∈ Z x – y ∈ Z
Distributive Property x × (y + z) = x × y + x × z x × (y − z) = x × y − x × z