It is not true.
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Whole numbers are positive numbers from zero to infinity. Integers are both positive and negative numbers. So whole numbers and integers have positive numbers in common, but only integers have negative numbers. Both have zero, and both have no fractions.
Positive integers are counting numbers, starting with 1. So: 1, 2, 3, 4 and so on.
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.
Integers are numbers that are not followed by decimals, so they are "complete" numbers. Numbers below zero are not positive, and zero itself is neither positive nor negative, so positive integers are 1, 2, 3, 4, 5, and so on. 1 is the smallest number of these, so it is the least positive integer.
Yes. Natural numbers are the counting numbers we use. Integers however contains also the negative values. So yes, natural numbers are integers, but the converse is not true though: integers are counting numbers is false.