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If x is a whole number, what other sets does x belong to?

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And we saw a couple of videos ago that I mentioned that the

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notion of the set of whole numbers is

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a little bit ambiguous.

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Sometimes whole number means non-negative integers.

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And sometimes it means all integers.

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But in this context, and I actually looked at what the

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writers of this question are looking for and the standards

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that they care about.

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So from their point of view, when they refer to whole

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numbers, they're referring to non-negative integers.

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So they're referring to 0, 1, 2, 3, so on and so forth.

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And I also looked at what they referred to-- And remember,

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this is just according to the writers of this question.

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This isn't according to how everyone views these things.

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But they view natural numbers as just the positive numbers.

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I told you two videos ago that some people view natural

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numbers as just the positive, but some people include 0 as a

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natural number.

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But in this context it's just the positive integers.

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I shouldn't have said positive numbers, I should have said

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positive integers.

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It obviously doesn't include the numbers

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in between the integers.

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So natural are there the numbers in this context.

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You'll see other contexts where this would be described

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as natural.

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In this context the natural numbers are 1, 2, 3, 4, so on

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and so forth.

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And of course, there's no ambiguity about what integers

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are; everyone agrees on that.

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Integers are-- you know, you could go arbitrarily negative

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and then negative 3, negative 2, negative 1, 0, 1, 2, 3.

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And you can just keep going in the positive direction.

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So if x is a whole number, when they say whole numbers

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they mean it is non-negative.

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What other sets does x belong to?

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Well, if it's a whole number, it's anyone of these numbers.

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And all of these numbers are also integers.

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The set of whole numbers, by the convention they're using,

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is this set right here.

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It is a subset of integers.

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So we know that x is also an integer.

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x is also a member of integers.

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That means a member, a member of a set.

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x is also a member of integers.

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But it will not be a member of natural numbers, or at least

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the way that they've defined it.

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Because x could be 0.

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0 is considered a whole number, but if x were 0, it

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would not be a member of the natural numbers.

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So we can't say it's natural.

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All we can say is, that it's definitely integers, it's

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definitely rational.

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Because any whole number, you can just divide it by 1 and

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represent it as a fraction.

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So x is a member of rationals.

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And of course, it's also a member of the real, which is

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the broadest set that we know of.

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