Set theory: Largest number in the set

[Cinitiator]

Homework Statement

How to write "the largest number in a set of real numbers A" using the appropriate set theory notation?

Homework Equations

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The Attempt at a Solution

Tried Googling and searching on Wikipedia with no relevant results.

 

[Dansuer]

What is the largest element of a set? Don't answer using the set theory notation, just English. Then try to convert your answer in set theory notation.

 

[vela]

Didn't Mark essentially answer this question in this thread?

 

[HallsofIvy]

Cinitiator seems to be mystified by the idea of the "maximum" operator.

 

[Cinitiator]

Cinitiator seems to be mystified by the idea of the "maximum" operator.

The thing is, the max operator in order statistics would only output the largest value of a set if that set is ordered from the largest one to the smallest one. One has to order the set in order to use this operator in order to find the largest real numbers. Now, I'm searching for a way to order a set from the largest to the smallest, without having access to any of its members.

Correct me if I'm wrong.

 

[alanlu]

Not all sets of real numbers have a largest element. Are you sure this is how the question is phrased?

Check out supremum.

Edit: Wait, I'm pretty sure Mark has answered your question in that thread.

 

[Cinitiator]

Not all sets of real numbers have a largest element. Are you sure this is how the question is phrased?

Check out supremum.

What I want to find are the min. and max. extremes of an ordered set which has a finite quantity of real numbers.

 

[alanlu]

min and max should work.

 

[Cinitiator]

min and max should work.

But how do I order a set before applying min and max? Of course, I could just do that manually, but let's say that I need an operator which would allow me to sort the set from the largest to the smallest in order to apply the min and max operators in a way which is relevant to my problem.

 

[alanlu]

I don't understand why you have to order a set if min and max are defined as the smallest and largest elements of a set.

Sets by definition don't have an order imposed on them. If you wanted to create an ordered n-tuple out of a set S of n elements, one way is to map it to the n-tuple (min S, min S \ {min S}, min S \ {min S, min S \ {min S}}, ...)

:P

 

[SteveL27]

But how do I order a set before applying min and max? Of course, I could just do that manually, but let's say that I need an operator which would allow me to sort the set from the largest to the smallest in order to apply the min and max operators in a way which is relevant to my problem.

The max is the max no matter what order you list the elements of the set. I explained this in the other thread you've got going on this topic.

Max{1,2,3,4} is the same as Max{4,2,3,1}.

In that other thread, someone actually posted C code to get the max of a set. And I pointed you to the bubble sort. Perhaps there is some secret context for your question that you're not telling us. Clearly you are not getting what you need despite a lot of people trying to answer your question.