You are correct with your definition of [0,1] x [0,1].
As for (x,x) x in [0,1] - Consider all the points that it forms (it will form a straight line with y = x where x is in [0,1]).
I have a question, what is the set ? What does it contain?
I know that, the unit interval is but then
is this true?
but then we must have
I was given the following set what is it and what does it contain? is it just a set of open intervals of the real line?
or is it a diagonal of the unit square?