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1/0 = 0 (2018)

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Re: 1/0 = 0 (2018)

#81

Post by [deleted] »

riwsky wrote: post #44
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…

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.

[deleted]

Re: 1/0 = 0 (2018)

#82

Post by bee_rider »

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, why pick the one very specific invalid value?

Re: 1/0 = 0 (2018)

#83

Post by sadeshmukh »

beala wrote: post #62
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.

Under what definition of division is (a/b)*b=a true for all values?

The one that excludes 0. It's not a terribly complicated thing to restrict domain: you don't expect, for example, complex values in real-valued functions.

Re: 1/0 = 0 (2018)

#84

Post by kstrauser »

I despise that answer because it’s so context-dependent. What’s? 10/10? 1. 5/5? 1. .3/.3? 1. .0000000578/.0000000578? 1.

Ergo, x/x=1, so 0/0=1. You can use the same logic for x/0=any rational number.

Defining x/0=0 is impossibly arbitrary.

Re: 1/0 = 0 (2018)

#85

Post by petesergeant »

riwsky wrote: post #44
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…

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.

Re: 1/0 = 0 (2018)

#86

Post by jraph »

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.

When we say "is not an allowable value", we are speaking about the domain [1]: all the values for which the function is defined. When we say "for all values", we implicitly mean for all values of the domain.

The parallel in programming would be the contract : you provide a function that works on a given set of values. Or the type: the function would "crash" if you passed a value not of the type of its parameter, but it is admitted it won't be done.

(In the remaining I'm referring to 1/x instead of a/b to simplify things a bit)

Another way of saying it is that the function is undefined for 0. (Or on {0}). Then the property is true for all values (on which the function is defined, but saying it is redundant, the function can't be called outside its domain, it is an error to try to do this).

The domain is often left out / implicit, but it is always part of the definition of a function.

0 is not in the domain, so it's not to be considered at all when studying the function (except maybe when studying limits, but the function will still not be called with it).

[1] https://en.m.wikipedia.org/wiki/Domain_of_a_function

Re: 1/0 = 0 (2018)

#87

Post by lilyball »

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.

Re: 1/0 = 0 (2018)

#88

Post by eqvinox »

v4vvdq wrote: post #15
CharlieDigital wrote: post #9

Earlier quoted context omitted.

There's a great Radiolab episode[0] that talks about divide by zero in perhaps more conceptual terms. KARIM ANI: If you take 10 and divide it by 10, you get one. 10 divided by five is two. 10 divided by half is 20. The smaller the number on the bottom, the number that you're dividing by, the larger the result. And so by that reasoning ... LULU: If you divide by zero, the smallest nothingness number we can conceive of…

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.

In IEEE 754 math, x/0 for x 
  >>> np.float64(-1.)/0.
  -inf
  >>> np.float64(1.)/0.
  inf
And you're exactly right, 0/0 is NaN in 754 math exactly because it approaches negative infinity, zero (from 0/x), and positive infinity at the same time.

Re: 1/0 = 0 (2018)

#89

Post by ilius2 »

clipsy wrote: post #54
ilius2 wrote: post #48

Earlier quoted context omitted.

That's nonsense. a/b is float in Python 3, and even in other languages a/b gets closer to it's actual value as a and b get bigger (the "limit", which is the basis of Algebra). So four operations in programming generally do agree with foundations of Algebra. But a/0=0 is %100 against Algebra. And it's very unintuitive. It's basically saying zero is the same as infinity, and therefore all numbers are the same, so why b…

> even in other languages a/b gets closer to it's actual value as a and b get bigger (the "limit", which is the basis of Algebra) This is not generally true. 5/2 = 2, 50/20 = 2, 500/200 = 2, and so on no matter how big the numbers get.

Yes, I meant when the result gets bigger. You get the idea.

Re: 1/0 = 0 (2018)

#90

Post by ilius2 »

sidpatil wrote: post #75
ilius2 wrote: post #50

Earlier quoted context omitted.

If you were to define a/0 the most logical choice would be a new special value "Infinity". The second best choice would be the maximum supported value of the type of a (int, int64 etc). Anything else would be stupid.

What if a is negative?

Same. Unless you want to differentiate -0 and +0 (which make it more complicated), you can not distinguish infinity from negative infinity.
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