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what is the supremum of a set with one element? watch

1. if X={a : a is in the reals} is supX=a?
2. No it wouldn't be. The set you have given is the set of real numbers. So saying Sup(X)=a doesn't make any sense as a just used to denote an element of the set not a specific number. It is the set of all numbers a such that a is a real number.

Note that Sup(X) doesn't necessarily exist.

Think about the set you are talking about, suppose that the set you have given has a supremum then that number we will call N has the property that N is greater than or equal to all elements of the set you have given and it is the smallest such number to have this property.

Now can you think of a number that is greater than or equal to every real number?

Hopefully you should see that the answer to the previous question would be no simply by the fact there are infinitely many real numbers.

Hence sup(X) can't exist.
3. (Original post by asdfyolo)
if X={a : a is in the reals} is supX=a?
I guess you meant something like ? What you have written is at best ambiguous.

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Updated: October 30, 2015
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