It is because that is how they are defined.
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We looked on-line for definitions of "integer", and every one we found
defined "integer" as meaning "whole number". So, yes.
All whole numbers are integers.
Yes all whole numbers are integers
Integers are all positive and negative whole numbers, and natural numbers are all positve whole numbers including zero. So, natural numbers is a subset of integers.
Yes integers are whole numbers
Always. By definition the Integers are the whole numbers; and the whole numbers are the integers.