i am trying to prove a set theory problem relating open and half open intervals. help needed.
1- [0,1] ~ (a,b)
2- [0,1] ~ [a,b)
3- [0,1] ~ (a,b]
where a,b belongs to R and ~ is equivalent sign.
for question 2, [0,1] ~ [a,b)
i have defined a function such that f(x) = (bx+a/2) / 2 for all x belongs to [0,1]. is that correct??