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1/0 = 0

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Re: 1/0 = 0

#121

Post by fasquoika »

whack wrote: post #72

My problem with "1/0 = 0" is that it's essentially masking what's almost always a bug in your program. If you have a program that's performing divide-by-zeroes, that's almost surely something you did not intend for. It's a corner case that you failed to anticipate and plan for. And because you didn't plan for it, whatever result you get for 1/0 is almost surely a result that you wouldn't want to have returned to the…

The real issue is that Pony doesn't have the concept of an unrecoverable error. All exceptions in Pony are checked, but sometimes if an error happens there's nothing your program can do and it should just crash.

Edit: Although Pony claims that programs should never crash, the language designers clearly understand the pragmatism of an unrecoverable error because it happens on OOM and stack overflow

Re: 1/0 = 0

#122

Post by avip »

whack wrote: post #72

My problem with "1/0 = 0" is that it's essentially masking what's almost always a bug in your program. If you have a program that's performing divide-by-zeroes, that's almost surely something you did not intend for. It's a corner case that you failed to anticipate and plan for. And because you didn't plan for it, whatever result you get for 1/0 is almost surely a result that you wouldn't want to have returned to the…

It’s common for 1/0 = 0 to be exactly what you want. Array average for example. That said raising exception would be the only consistent behavior if a language supports that.

Re: 1/0 = 0

#123

Post by lmm »

ASalazarMX wrote: post #46
pmiller2 wrote: post #19

Earlier quoted context omitted.

It is inconsistent. If 1/0 = 0, then 1 = 0*0.

Wait, if 1 / 0 = infinity, then infinity * 0 = 1 This seems just as bizarre, since zero times anything shouldn't become 1, no matter how big or how many times you do it.

> This seems just as bizarre, since zero times anything shouldn't become 1, no matter how big or how many times you do it.

It isn't bizarre, because there's an equal and opposite argument that anything times infinity is infinity, no matter how small the thing you multiply by.

If you actually do infinity * 0 you get NaN since there's no way to determine (without more information) whether the result should be 0, infinity, or anything in between.

Re: 1/0 = 0

#124

Post by emileokada »

It's quite staggering how many people have posted on this thread without reading the article. Nearly all the objections people have raised are directly addressed in the post.

For those who still object to the argument, would you object to me defining the piecewise function f:R->R defined to be 1/x for x =/= 0 and 0 for when x=0?

Re: 1/0 = 0

#125

Post by kazinator »

> Lawrence Paulson:

> > These things are conventions, exactly the same as announcing that x^-n = 1/x^n and that x^0 = 0.

Say what? x^0 is 1, and not by convention, other than in the 0^0 = 1 case.

Re: 1/0 = 0

#126

Post by lmm »

FlipperBucket wrote: post #14
luso_brazilian wrote: post #7

> But is Pony doing something unsound? Absolutely not. It is totally fine to define 1/0 = 0. Nothing breaks It actually does break something, the symmetry between division and multiplication and the many pieces of code that assume that (x / y) * y equals x. Here is a naive and non practical example, but it is not impossible to find a real world example where this simplified code manifests itself accidentally or by de…

> the many pieces of code that assume that (x / y) * y equals x The same issue if division by zero throws an exception. This is simply a more practical approach that dispenses with the exception handling (ie becomes a less irregular test case). Edit: Not buggy behavior, when expected.

Assuming an exception is equivalent to any non-exceptional value doesn't break anything. See "Fast and Loose Reasoning is Morally Correct".

Re: 1/0 = 0

#127

Post by magicalhippo »

avip wrote: post #122
whack wrote: post #72

My problem with "1/0 = 0" is that it's essentially masking what's almost always a bug in your program. If you have a program that's performing divide-by-zeroes, that's almost surely something you did not intend for. It's a corner case that you failed to anticipate and plan for. And because you didn't plan for it, whatever result you get for 1/0 is almost surely a result that you wouldn't want to have returned to the…

It’s common for 1/0 = 0 to be exactly what you want. Array average for example. That said raising exception would be the only consistent behavior if a language supports that.

And in other cases you really do want the infinities. For example fast ray-AABB tests like https://tavianator.com/fast-branchless-raybounding-box-inter...

Re: 1/0 = 0

#128

Post by cuspycode »

The article uses two example theorems to justify this: a * (b/c) = b * (a/c), which can be extended to cover the c=0 case, and a/a = 1, which can be extended to cover the a=0 case. I can see how this can be useful in some situations, but it's not natural in the same way as e.g. analytical continuations of complex functions are.

Re: 1/0 = 0

#129

Post by drb91 »

avip wrote: post #122
whack wrote: post #72

My problem with "1/0 = 0" is that it's essentially masking what's almost always a bug in your program. If you have a program that's performing divide-by-zeroes, that's almost surely something you did not intend for. It's a corner case that you failed to anticipate and plan for. And because you didn't plan for it, whatever result you get for 1/0 is almost surely a result that you wouldn't want to have returned to the…

It’s common for 1/0 = 0 to be exactly what you want. Array average for example. That said raising exception would be the only consistent behavior if a language supports that.

Common compared to what? Taking an average of an empty array is nonsensical.

Re: 1/0 = 0

#130

Post by krylon »

Once a mathematician explained to me in mind-numbing detail why dividing by zero is impossible, so I understand why this is gross better than I ever wanted to.

But having said that, I do not remember when I last saw a Divide-by-Zero-error in the wild. In practical terms, this is the last kind of bug I worry about.

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