For anyone who is familiar with the concept of smooth world (from Bell), is the identity function $f(x)=x$ continuous in that world? Cheers!
2026-02-22 19:47:18.1771789638
Identity function on a smooth world
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Yes, the identity function is continuous. That's because if $\Delta x$ is infinitesimal, then also $\Delta x$ is always infinitesimal.