00:01
In this question, we have been asked is the ordered set of even numbers an infinite sequence, and we have to explain why or why not.
00:08
So the answer to this is yes, the ordered set of even numbers is an infinite sequence.
00:16
Intuitively, if we think about this, there are an infinite number of even numbers.
00:21
So because of that, this will be an infinite sequence.
00:25
And if we want to provide a proof, let us prove this by contradiction.
00:29
Let us assume that the set is a, the ordered set is a finite sequence.
00:37
So if it is a finite sequence, then this ordered set of even numbers should have a largest element.
00:43
So let us assume that the element is m.
00:47
So that will mean that m is the largest even number, which will mean that any number, which is greater than m, this will mean that any number, this will not be an even number, this must be an odd number.
01:03
So that will mean that m plus 1, an m plus 2, m plus 3 and so on, all of these numbers need to be odd.
01:11
However, if m is an even number, then the next number after that must be odd...
