Comment on I just cited myself.

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barsoap@lemm.ee ⁨4⁩ ⁨months⁩ ago

Decimals require you to check the end of the number to see if you can round up, but there never will be an end.

The character sequence “0.999…” is finite and you know you can round up because you’ve got those three dots at the end. I agree that decimals are a shit representation to formalise rational numbers in but it’s not like using them causes infinite loops. Unless you insist on writing them, that is. You can compute with infinities just fine as long as you either a) bound them or b) keep them symbolic.

That only breaks down with the reals where equality is fundamentally incomputable. Equality of the rationals and approximate equality of reals is perfectly computable though, the latter meaning that you can get equality to arbitrary, but not actually infinite, precision.

…sometimes I do think that all those formalists with all those fancy rules about fancy limits are actually way more confused about infinity than freshman CS students.

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