Comment by lupire | Hacker News Reader

Comment by lupire | Hacker News Reader

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Because 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.

Sure.. 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.

Consider 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.

> 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.

For example, zero is the only real infinitesimal value.

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