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Nov 13 at 9:54 comment added Najib Idrissi @bof Yes, there are tons of examples.
Nov 13 at 0:24 comment added bof Or $f(P)=g(\#P)$ where $g:\omega\to\{0,1\}$ is any nonconstant function. Or $f(P)=1$ if $\#P=\min P$ and $f(P)=0$ otherwise.
Nov 12 at 14:39 vote accept Dominic van der Zypen
Nov 12 at 12:50 history answered Najib Idrissi CC BY-SA 4.0