Question

@experimentX What's the \(\max\) or \(\min\) of a set?

Answer 1

Is it just the maximum or a minimum number?

Answer 2

first of all, you should talk about boundedness of set. there are two bounds ... upper bound (this may or may not have max element)
for example ... consider this set {x:x<2}
and consider this set {x:x\( \le 2\)}

Answer 3

both cases, there are upper bounds, but first case, you do not have maximum element while second case you have maximum element.

similarly you can define minimum element.

Answer 4

Oh, I see -- got it :D

Answer 5

So \(\max\{x:x\le 2\} = 2\), right?

Answer 6

yep!!
but we can extend a concept called Supremum or Lowest upper bound when the set is open.

Answer 7

@experimentX But that would only work if we're working in \(\mathbb{R}\) or \(\mathbb{Q}\) right?

Answer 8

So, can I assert the following?\[\max\{x:x<2\},x\in\mathbb{N} = 1\]

Answer 9

yep!! if we are working on Integers, then if the set is bounded, then there will always be maximum or minimum element depending on boundedness.

Answer 10

+1, another great answer :-)

Answer 11

about that .. yes you can assert
\[ \max\{x:x<2 \text{ and } x\in\mathbb{N}\} = 1\]
thanks!!