Let $X$ and $Y$ be sets, and $f:X\to Y$ be a function. Is there a name for the following quantity? $$\sup_{y\in Y}\ \big|f^{-1}(y)\big|$$
I was thinking the "maximal valence of $f$".
2026-04-25 22:16:27.1777155387
Name for the maximum size of $f^{-1}(w)$
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I don't think I would use the word "valence" here! In any case, you say "let X and Y be sets" but are you assuming that these are number sets? For general set "A" neither | | nor "sup" exists.