How many functions from $[0, 1]$ to $[0, 1]$ have a left-sided limit at every point? There is at least $|\mathbb{R}|$ of them, since $f(x) = rx, r \in \mathbb{R}$ obviously works. How can I show that there is no more than $|\mathbb{R}|$ of such functions?
2026-04-02 09:54:12.1775123652
How many functions from $[0, 1]$ to $[0, 1]$ have a left-sided limit at every point?
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