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No. Natural numbers are 0, 1, 2, 3 ... If a was defined to be a negative integer, then -a would equal a natural number. But -a is a variable with a sign, not a natural number.
Yes, all natural numbers are real numbers. Natural numbers are a subset of real numbers, so not all real numbers are natural numbers.
No. Natural numbers are a subset of whole numbers. Negative numbers are whole numbers but not natural.
All of the natural numbers.
Yes. All natural numbers are rational numbers.