The answer to the question depends on what property of positive numbers the question is about.
If your question is a case of adding random apostrophes, then the answer is yes, they do include oll positive integers. - No apostrophe required.
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Actually the set of integers is the same as the set of whole numbers since the whole numbers include negative whole numbers and zero.
No, integers are positive and negative whole numbers
Natural numbers are sometimes defined to include zero, sometimes not. Equivalent terms therefore may include: positive integers, non-negative integers, whole numbers, positive whole numbers ("whole number" is ambiguous; some take it to include negative numbers, some not).
No. All numbers greater than zero are positive real numbers. Integers are whole numbers (positive or negative) and therefore, don't include numbers with decimals.
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.