Q:

How do i prove this from Continuum hypothesis?

Under ZFC, let's assume Continuum hypothesis

There exists an well-ordered set $W$ and a bijection $f:[0,1]\rightarrow W$ such that $\forall x\in[0,1]$, $f(x)$ has at most countable predecessors in $W$

How do i prove this?

A:

HINT: Take the least possible well-ordering of $[0,1]$. 

