nostr:nprofile1qy2hwumn8ghj7un9d3shjtnyd968gmewwp6kyqpqjvrljj4jyvuwkflq2ucxerruprum6lj2ju4kjzp3gtaawf42uefsd2l2x5 Granted, I don't have the time right now to watch the whole thing, but the initial imp...
@nprofile1q... The hyperreal numbers extend the real number line to include infinities (defined in terms of omega, an infinite number strictly greater than every real number) and infinitesimals (defined in terms of epsilon, or 1 over omega).
The closest thing to a limit would be the standard part function st(), which just takes the closest real number to a finite hyperreal number. The hyperreal definition of e is just st( (1+epsilon)omega ).
If you ever wondered why you could treat infinity as a number and it almost always works, you were just using a less formal version of hyperreals. The formal version fixes the cases where it doesn't work.
In the hyperreal domain, 0.9 repeating is not 1, but the standard part of 0.9 repeating is.
The closest thing to a limit would be the standard part function st(), which just takes the closest real number to a finite hyperreal number. The hyperreal definition of e is just st( (1+epsilon)omega ).
If you ever wondered why you could treat infinity as a number and it almost always works, you were just using a less formal version of hyperreals. The formal version fixes the cases where it doesn't work.
In the hyperreal domain, 0.9 repeating is not 1, but the standard part of 0.9 repeating is.
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