Yes. The integers include all of the positive and negative whole numbers and zero.
Whole numbers, natural numbers, counting numbers are all types of integers.
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It depends on what you consider a natural number. If you consider it to be the set of all integers starting from 1 and going upward, then no, 0 is not a natural number.
However, if you consider a natural number to be the set of all non-negative integers, then 0 is included in the set of natural numbers.
Most math scholars do not consider zero a natural number. Natural number are also known as counting numbers such as 1,2,3,4,5….