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1/0 = 0 (2018)

hillelwayne.com

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Re: 1/0 = 0 (2018)

#91

Post by snickerbockers »

lilyball wrote: post #87
codeflo wrote: post #12

This article invents a new binary operation, calls it "division" and uses the "/" operator to denote it. But the article repeats multiple times that this new operation isn't a multiplicative inverse, so it's not actually division. For example, (a/b)*b=a isn't true for this new operation.

(a/b)*b=a isn't true, but that's also not true for the math that you're thinking of. What is true is IF b≠0 THEN (a/b)*b=a. And this definition works just fine even if you define division by zero. Also just to point out, the statement here really is a*b‾*b=a, which might make it more clear why b≠0.

There's no "if" in the division operation. Division is not defined for b=0. a/0 is a nonsensical quantity because the zero directly contradicts the definition of division.

maybe someday there will be a revelation where somebody proposes that it's a new class of numbers we've never considered before like how (1-1), (0-1) and sqrt(-1) used to be nonsensical values to past mathematicians. For now it's not defined.

Re: 1/0 = 0 (2018)

#92

Post by worik »

Division has an intuitive meaning: A divided by B is the number of Bs in A.

That is an intuition why division by zero is undefined.

Defining it arbitrarily is uninteresting.

Disapointing

Re: 1/0 = 0 (2018)

#93

Post by worik »

petesergeant wrote: post #85
riwsky wrote: post #44

Earlier quoted context omitted.

Huh? The article shows why 1/0=0 is mathematically sound, and then considers an error preferable in a programming context anyway, because practicality. It’s the opposite of the reasoning you’re describing.

> The article shows why 1/0=0 is mathematically sound It does not, because it is not. And the “real mathematicians” that he quotes aren’t supporting his case either, they’re just saying that there are cases where it’s convenient to pretend. If you look at the Wikipedia page for division by zero you may find “it is possible to define the result of division by zero in other ways, resulting in different number systems”:…

> in short, if it’s convenient, you can make up your own rules.

Yes.

People find it confusing that there is no simple model that encapsulates arithmetic. Fields do not capture it in its entirety. The models of arithmetic that describe it end up being extremely complex.

Arithmetic is ubiquitous in proofs of other things, and people like the author of this blog cannot get over it.

Reality is weird, inconsistent, and weirdly incomplete.

Get used to it!

Re: 1/0 = 0 (2018)

#94

Post by worik »

bee_rider wrote: post #82

Maybe division by zero should just not exist. If you actually write 1/0 in a manner that can be discovered through static analysis, that could just be a compile time error. If you compute a zero, and then divide by it… I dunno. Probably what happened was the denominator rounded or truncated to zero. So, you actually have 1/(0+-e), for some type-dependent e. You have an interval which contains a ton of valid values, w…

> Maybe division by zero should just not exist.

It does not. It is undefined

Re: 1/0 = 0 (2018)

#95

Post by zzo38computer »

In uxn, the result of division of anything by zero is defined as zero (there are no error conditions in uxn). I did not know that Pony is also doing that. This is not a proper "division" (since it is not always a multiplicative inverse operation), but it does not necessarily have to be (and, as another comment mentions, the integer division operator in many programming languages is not a proper "division" either); it is something else which might use a "/" sign or the instruction name "DIV" or whatever.

Re: 1/0 = 0 (2018)

#96

Post by zzo38computer »

beala wrote: post #72
mjcohen wrote: post #68

Earlier quoted context omitted.

If 0 is not an allowable value for b is necessary but not generally sufficient.

Can you say more? If "0 is not an allowable value for b", then it seems to me that (a/b)*b=a isn't true for all values. Specifically, it's false when b=0. IIUC, codeflo is arguing that the division operation defined in the article isn't "actual division" because (a/b)*b=a isn't true for all values. But I can't think of a definition of division that satisfies that criteria.

If "0 is not an allowable value for b", then (a/b)*b=a is not defined when b=0, so it is neither true nor false, since you had previously agreed that b=0 is not allowed (regardless of what "/" and "*" are meaning in this context).

Re: 1/0 = 0 (2018)

#97

Post by pasquinelli »

sethev wrote: post #18

I debated this with my boss at my first programming job (this was 20+ years ago). He thought 1/0 should be 0 rather than an error because "that's what people expect". My argument was from mathematical definitions (the argument which this blog post picks apart). In retrospect, I see his point better - practical use trumps theory in most language design decisions. I haven't changed my mind but the reason has shifted mo…

i would not expect 1/0 to be zero. as you divide by smaller numbers, the quotient gets bigger, so i can't understand why someone would expect /0 to be zero.

Re: 1/0 = 0 (2018)

#98

Post by pasquinelli »

WithinReason wrote: post #16
v4vvdq wrote: post #15

Earlier quoted context omitted.

Then take 10 and divide it by -10 = -1. 10 / -5 = -2. 10 / -0.5 = -20. So from the other side of the y-axis it behaves the exact opposite. It goes to minus infinity. So at x=0 we would have infinity and minus infinity at the same time. Imho that is why it is undefined.

on computers you can have negative zeros

that's really just an encoding of the number to help you understand how the hell you got here

Re: 1/0 = 0 (2018)

#99

Post by throwawaymaths »

Yes, it's all good and nice that your types are sound and you don't have panics, but I feel like this could get you in trouble in the real world (gleam also uses this division convention, and people very much use gleam for "real world" things). Suppose you took an average over an unintentionally empty list (maybe your streaming data source just didn't send anything over the last minute due to a backhoe hitting a fiber in your external data source's data center) and took some downstream action based off of what you think is the rolling average. You could get royally fucked if money is involved.

Crashing would have been preferable.

1/0 = 0 is unsuitable and dangerous for anyone doing anything in the real world.

Re: 1/0 = 0 (2018)

#100

Post by renewiltord »

rsp1984 wrote: post #31
lupire wrote: post #8

Earlier quoted context omitted.

It's fine. Infinity isn't a real number, so 1/x isn't continuous at 0, so it doesn't matter what the value of 1/0 is. All your open sets still behave the way you expect. Whether you choose "this function is undefined here" vs "it's impossible to ever reach the value of this function at this value, under any assumptions I'll ever care about" is purely a matter of convenience.

Yea, but conceptually it's a bit smelly to have f(x) get larger and larger the closer x is to 0 and then suddenly have it be 0 once x reaches 0.

But once you go behind, it flips suddenly anyway so you could just as well have it be intuitively “halfway between the positive and negative infinities” which is at least fun and could spawn a few “Why is 1/x suddenly go to zero” articles on HN in 2053
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