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Why does every integer have an opposite?
The numbers 1,2,3,... etc are called natural numbers or counting numbers. Integers are the natural numbers plus zero plus the negative ( or opposite ) natural numbers. Why do we need negative natural numbers ? For one thing x + 1 = 0 is an equation whose solution is x = -1. We could not solve this equation if we did not have negative integers. So over history these negative numbers came about as a way to solve certain math problems. The numbers 1,2,3,... etc are called natural numbers or counting numbers. Integers are the natural numbers plus zero plus the negative ( or opposite ) natural numbers. Why do we need negative natural numbers ? For one thing x + 1 = 0 is an equation whose solution is x = -1. We could not solve this equation if we did not have negative integers. So over history these negative numbers came about as a way to solve certain math problems.
Are natural numbers real numbers?
Yes, all natural numbers are real numbers. Natural numbers are a subset of real numbers, so not all real numbers are natural numbers.
Do set of natural numbers contain sets of whole numbers?
No. Natural numbers are a subset of whole numbers. Negative numbers are whole numbers but not natural.
What numbers are in the set of natural numbers and which are in the set of whole numbers?
All of the natural numbers.
Rational numbers are sometimes natural numbers?
Yes. All natural numbers are rational numbers.
