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Hausdorff distance property

Hi. About a month ago you added something to the Hausdorff distance page, claiming that "If $X\subset Y$, then $d_{\mathrm {H} }(X,Z)\geq d_{\mathrm {H} }(Y,Z)$". Unless I'm confused, this just isn't true -- the corresponding inequality holds for one of the two things whose max is the Hausdorff distance, so to speak, but not for their maximum. (Suppose X=Z={1} and Y={1,2}. Then $d_{\mathrm {H} }(X,Z)=0$ and $d_{\mathrm {H} }(Y,Z)=1$. I haven't changed the page itself yet, just put a note on its talk page, because I wanted to check whether maybe there's some other true thing that you meant to write instead :-). Or maybe I am in fact confused and the claim is true after all. (I'm away from my usual computer hence not logged in right now, but I'm Gareth McCaughan.) 15.90.166.11 (talk) 13:13, 5 January 2024 (UTC)

I've removed it from the page now that I'm able to do so as myself. If I'm missing something, do let me know :-). Gareth McCaughan (talk) 02:31, 8 January 2024 (UTC)