Minimum Element
Calculus
Level
2
I have 2 sets such that
- the elements of both these sets are all positive numbers;
- one of them has infinitely many elements, while the other has finitely many elements.
The finite set has a minimum element, that is, there exists an element in the set such that every other element in the set is greater than it.
Will the infinite set also have a minimum element?
No, not necessarily
Yes, always
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
As a counterexample, the set (1, 0.1, 0.01, 0.001,... ) has no minimum element because every is smaller than the previous one.