Denoting the Largest Member of a Set: Symbols & Techniques

[bomba923]

Let's say I have a set {A}. How do I denote the largest member of that set?
For example, let's say I have a solution set of discrete values. How do I denote the largest solution?

Basically, with any set, how do I denote the largest member of that set? What symbol/s do I use !?

 

[arildno]

What's wrong with something like max(A)??

 

[bomba923]

That is the formal/accepted way of expressing it (the largest member of a set), right?

 

[honestrosewater]

Do maximums differ from least upper bounds (supremums)? The definitions I found didn't clear this up. Edit: Eh, because I was going to say supremum.

 

[Muzza]

AFAIK, the maximum of a set must necessarily be a member of the set as well. So for example, {1 - 1/n; n a natural} has a supremum, but no maximum.

 

[matt grime]

Muzza is absolutely correct.

given a set (presumably of real numbers) there is no reason for that set to even have a greatest element, even if it is bounded above (ie all elements are less than some constant K). The sup is the smallest such K that bounds them above, and this is the max if and only if K is an element of the set.

Note, that this only applies to infinite sets. Any finite set of points must have a maxmimum.