Number sets
Number Sets 3 Number Sets 3
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- If x is a whole number, what other sets does x belong to?
- And we saw a couple of videos ago that I mentioned that the
- notion of the set of whole numbers is
- a little bit ambiguous.
- Sometimes whole number means non-negative integers.
- And sometimes it means all integers.
- But in this context, and I actually looked at what the
- writers of this question are looking for and the standards
- that they care about.
- So from their point of view, when they refer to whole
- numbers, they're referring to non-negative integers.
- So they're referring to 0, 1, 2, 3, so on and so forth.
- And I also looked at what they referred to-- And remember,
- this is just according to the writers of this question.
- This isn't according to how everyone views these things.
- But they view natural numbers as just the positive numbers.
- I told you two videos ago that some people view natural
- numbers as just the positive, but some people include 0 as a
- natural number.
- But in this context it's just the positive integers.
- I shouldn't have said positive numbers, I should have said
- positive integers.
- It obviously doesn't include the numbers
- in between the integers.
- So natural are there the numbers in this context.
- You'll see other contexts where this would be described
- as natural.
- In this context the natural numbers are 1, 2, 3, 4, so on
- and so forth.
- And of course, there's no ambiguity about what integers
- are; everyone agrees on that.
- Integers are-- you know, you could go arbitrarily negative
- and then negative 3, negative 2, negative 1, 0, 1, 2, 3.
- And you can just keep going in the positive direction.
- So if x is a whole number, when they say whole numbers
- they mean it is non-negative.
- What other sets does x belong to?
- Well, if it's a whole number, it's anyone of these numbers.
- And all of these numbers are also integers.
- The set of whole numbers, by the convention they're using,
- is this set right here.
- It is a subset of integers.
- So we know that x is also an integer.
- x is also a member of integers.
- That means a member, a member of a set.
- x is also a member of integers.
- But it will not be a member of natural numbers, or at least
- the way that they've defined it.
- Because x could be 0.
- 0 is considered a whole number, but if x were 0, it
- would not be a member of the natural numbers.
- So we can't say it's natural.
- All we can say is, that it's definitely integers, it's
- definitely rational.
- Because any whole number, you can just divide it by 1 and
- represent it as a fraction.
- So x is a member of rationals.
- And of course, it's also a member of the real, which is
- the broadest set that we know of.
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