Question #2634

1) Is all whole numbers are natural numbers ?
2) Is whole numbers are integers ?

Expert's answer

To answer the questions it is necessary to specify the definition of the term whole numbers, which in fact does not have a consistent definition.& Various authors use it in one of the following senses

* the nonnegative integers (0, 1, 2, 3, ...)

* the positive integers (1, 2, 3, ...)

* all integers (..., -3, -2, -1, 0, 1, 2, 3, ...)

The following definitions are standard:

& Natural numbers are

& {1,2,3,…}

Integer numbers are

{…-2.-1,0,1,2…}

Perhaps whole numbers in this question are {0,1,2,…}

In this case

The answer to 1) is NO, while the answer to 2) is YES.

* the nonnegative integers (0, 1, 2, 3, ...)

* the positive integers (1, 2, 3, ...)

* all integers (..., -3, -2, -1, 0, 1, 2, 3, ...)

The following definitions are standard:

& Natural numbers are

& {1,2,3,…}

Integer numbers are

{…-2.-1,0,1,2…}

Perhaps whole numbers in this question are {0,1,2,…}

In this case

The answer to 1) is NO, while the answer to 2) is YES.

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