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Honestly this hurts my head but Hillel is inevitably correct. You can define an explicitly undefined operation to do whatever you like. But what’s the point? Th
by moomin 2y ago
Honestly this hurts my head but Hillel is inevitably correct. You can define an explicitly undefined operation to do whatever you like. But what’s the point? There’s no new mathematics you can do with it, no existing behaviours you can extend like this. Normally, when you divide by a small number, you get a large number. Now for some reason it goes through zero. Why not five? Why not seven?
Just because it’s formally consistent doesn’t mean it isn’t dumb.
- lupire 2y agoBecause exceptions are expensive, and functions with holes are dumb. "Dumb" is purely a matter of aesthetic preference. Calling things "dumb" is dumb. > Normally, when you divide by a small number, you get a large number. Now for some reason it goes through zero. Zero is not a "small" number. Zero is the zero number. There is no number that is better result than 0 when dividing by 0; "Infinity" is not a real (or complex) number. This itself is GREAT reason to set 1/0 = 0. It only ever bothers people who conflate open sets with closed sets, or conflate Infinity with real numbers, so it's good have this pop up to force people to think about the difference.
- recursive 2y ago> Zero is not a "small" number. Zero is the zero number. What do you mean by this? Zero is certainly a zero number, but it seems that it might also be a small number simultaneously.
- thaumasiotes 2y agoFor example, zero is the only real infinitesimal value.
- akira2501 2y agoSure.. but there are infinite series that sum to a finite value. Perhaps a pertinent example would be summing all the distances between each successive reciprocal of 1: Sum[1/x - 1/(x+1), {x, 1, ∞}] == 1 You do actually need infinity to arrive at that 1.
- moomin 2y agoConsider that lim -> inf does not mean “It goes to infinity”. Its actual definition has nothing to do with infinity. So your argument about infinity is a red herring. Or try it the other way, tell me what mathematics works better if 1/x=0 than 1/x=5. If there’s an aesthetic preference displayed here, it’s for mathematics as a tool for reasoning.
- deleted 2y ago[deleted]