M = set
Statement: This set does not have a supremum in
Prove with contradiction:
Let's say there is an
Then we can assume each of the following 3 options:
, can't be true because we know is not in (won't prove that now..)
Here's where I get stuck..
Let's say there is a so that
So we want that
Then we say
This applies only if
That's what we had done at uni but I don't understand the last 2 paragraphs..
I know if we square a number that is less than 1 that we get a number that is less than the number we squared so I get it why the 'h' in brackets is replaced by 1.. but how do you know for sure that is still less than 2?