Problems 1234 Brief explain please It is about math Analysis

Solution

1) A is a subset of R and each element of a <L for some real R.

Then the statement is true.

Since L is not in A, sup cannot be equal to L

So supremum of A <L

2) False. Irrational numbers cannot be ordered and not countable.

Hence bijectin from N to R\\Q is not possible

3)