# Closure in natural numbers whole numbers

The natural numbers appear within the set of whole numbers. in this set of numbers. • The natural numbers are "closed" under addition and multiplication. For example, take any two natural numbers, say 3 and 9. Now, 3 + 9 = 12 is a natural/whole number. Therefore, the system is closed under addition. In this lesson, we explore what it means to say whole numbers and integers are closed under the mathematical operation of addition.

Rational Numbers: This set is closed under addition, subtraction, Whole Numbers: Subtraction requires negative integers; division requires rational numbers. What you need to do is state which topological space the natural numbers are a subset Originally Answered: How are sets of natural numbers closed? Why isn't the set of whole numbers bigger than the set of natural numbers, if the whole . To be able to prove something about addition, you would first have to define it. And the sum of two natural numbers, however you define it, is a.

A set has closure under an operation if performance of that operation on members of the set always produces a member of the same set; in this case we also say that the set is closed under the operation. For example, the positive integers are closed under addition, but not under. There are different kinds of numbers, of course: whole numbers, integers, rational and irrational, real and complex, etc Some of these sets are described in the. For example, the whole numbers are closed under addition, The integers are closed under multiplication (if you multiply two integers, you get.

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