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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 ex

by sethev 2y ago

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 more toward because "it's what a larger set of people expect in more situations" rather than mathematical purity.

riwsky 2y ago
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 2y ago
  [deleted]
- petesergeant 2y ago
  > 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.
  - worik 2y ago
    > 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!
  - Attrecomet 2y ago
    "Making up your own rules" is literally what mathematics is, though. Using that as a counterargument to using a specific set of axioms tells me you don't understand mathematics.
    - Scarblac 2y ago
      But adopting a rule that says 1/0 = 0 means you may also have to accept that 1 = 0*0.
    - ConspiracyFact 2y ago
      >”Making up your own rules" is literally what mathematics is, though. We don’t make up arbitrary rules, though. Well…so-called mathematicians who study systems with completely arbitrary rules are just jerking off. The rules that most mathematicians use are based on our intuitions about what can’t be proven but “has to be” true.
pasquinelli 2y ago
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.
- iforgotpassword 2y ago
  If I have five apples and were to divide them among 0 people then nobody gets anything and I can eat them all, so the proper solution would be 5.
  - Almondsetat 2y ago
    you can't divide the apples among 0 people and then claim to still have them, because in that case you would have divided them among 1 people
    - dmz73 2y ago
      Like everything in life, it depends... For example: Storage has 5 items that need to be processed. 5 items need to be split equaly between available processes. There are currently 0 available processes so 5 / 0 = 0 items to be processed is more correct than either 5 or Nan or infinity.
      - Almondsetat 2y ago
        Your example is quite vague (e.g. are we dealing with an integer number of items and processes?) and in general if something looks kinda like a division it doesn't mean it is exactly division. Just like in math, we have the power to simply say: if COND -> divide normally, else -> do something else.
    - postalrat 2y ago
      And that's why the answer is 0.
  - askvictor 2y ago
    Paraphrasing you: "If I have five apples and were to divide them among 0 people, how many does each person get?" This sums up one approach to this problem, and can be thought of in a more intuitive manner than the limit approach. The answer could be zero. Or 1. Or 37. In fact, any number makes as much sense as the question. Which is why either an exception is raised, (or +- Inf is returned for floats, but that's just the limit approach). But perhaps it would be more fun just to return a random number on divide by zero :)
throwawaymaths 2y ago
1/0 = 0 is usually not a practical thing, it's to satisfy that the output of the division operator stays in the type and you don't want crashes (a "feature" of ponylang and gleam, e.g.). Its kind of a PL wonk thing. It's not at all a good idea for very important practical reasons as I outline in a reply to parent.
- ncruces 2y ago
  I don't want to handle errors after every division and division doesn't crash, both sound rather practical, though.
  - AlotOfReading 2y ago
    The original purpose of defining it to be Nan/INF in floating point was exactly that. You'd do all the work and then check if it was Nan/INF at the end without having to check every intermediate result.
    - eru 2y ago
      If you want to do all the work at the end, 'exceptions' do exactly that, too.
      - davorak 2y ago
        Throwing an exception in a function normally stops the rest of the work that function would do. That is not the case when using Inf and similar > const f = (x) => [x/2, x/0] undefined > f(10) [ 5, Infinity ]
        NBJack 2y ago
        I assert stopping immediately is much more practical. In many cases, you waste considerable amounts of processing power to reach a conclusion you often won't be able to use.
deleted 2y ago
[deleted]
jsnedjdn 2y ago
Never have I ever met anybody who would think dividing by zero yields zero O_o If anything it feels natural to yield +/-infinity
- giraffe_lady 2y ago
  It's not about what I think zero division yields I've taken a math class before. It's just about representation within the type system. If division can return infinities we can't safely combine division with other functions that are expecting ints and floats. Most languages throw an error instead, but there are tradeoffs there too. If you've decided not to throw an error you should at least return a usable number and zero makes more sense than -1 or 7 or a billion or whatever. You could also build the number stack from the ground up to accommodate this edge case, and make it so all arithmetic functions can handle infinities, infinitesimals and limits. I've come across a racket sublang like that but it's nearly unusable for the normal common things you want to do with numbers in code.
  - ctenb 2y ago
    NaN is a valid float, so are infinities
    - giraffe_lady 2y ago
      They're valid according to a spec that doesn't mean I want one showing up when I'm trying to calculate the area of a semicircle or whatever. In the context of getting one by surprise in simple arithmetic they are approximately as bad as zero. Either way you have to decide how to handle it and there are tradeoffs of different approaches, as the article discusses. It's not about someone just being ignorant of basic math like the comment I was replying to implied.
      - morningsam 2y ago
        >In the context of getting one by surprise in simple arithmetic they are approximately as bad as zero. I don't think so, because getting 0 in a larger expression might yield a result that looks plausible, leading to hidden bugs. Inf and NaN both are good because they necessarily propagate all the way up to the end result, making it obvious that something went wrong.
JumpCrisscross 2y ago
> He thought 1/0 should be 0 rather than an error because "that's what people expect" So I saw this in action once, and it created a mess. Private company had a stupid stock dividend mechanism: every shareholder received some fraction, dependent on fundraising, of a recurring floating pool of shares, quantity dependent on operating performance. (TL; DR Capital was supposed to fundraise, management was supposed to operate. It was stupid.) One quarter, the divisor was zero for reasons I can't remember. This should have resulted in no stock dividend. Instead, the cap-table manager issued zero-share certificates to everyone. By Murphy's Law, this occured on the last quarter of the company's fiscal year. Zero-share certificates are used for one purpose: to help a shareholder prove to an authority that they no longer own any shares. Unlike normal share certificates, which are additive, a zero-share certificate doesn't add zero shares to your existing shares; it ambiguously negates them. In essence, on that day, the cap-table manager sent every shareholder a notice that looked like their shares had been cancelled. Because their system thought 1 / 0 = 0. If you're dividing by zero in a low-impact system, it really doesn't matter what you output. Zero. Infinity. Bagel. If you're doing so in a physical or financial or other high-impact system, the appropriate output is confused puppy.
deleted 2y ago
[deleted]
makr17 2y ago
I remember my junior high maths well enough, allowing division by zero is an essential step in proving that 1 == 2, which we _definitely_ don't want.

by sethev 2y ago

riwsky 2y ago

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 2y ago
[deleted]
petesergeant 2y ago
> 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.
- worik 2y ago
  > 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!
- Attrecomet 2y ago
  "Making up your own rules" is literally what mathematics is, though. Using that as a counterargument to using a specific set of axioms tells me you don't understand mathematics.
  - Scarblac 2y ago
    But adopting a rule that says 1/0 = 0 means you may also have to accept that 1 = 0*0.
  - ConspiracyFact 2y ago
    >”Making up your own rules" is literally what mathematics is, though. We don’t make up arbitrary rules, though. Well…so-called mathematicians who study systems with completely arbitrary rules are just jerking off. The rules that most mathematicians use are based on our intuitions about what can’t be proven but “has to be” true.

pasquinelli 2y ago

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.

iforgotpassword 2y ago
If I have five apples and were to divide them among 0 people then nobody gets anything and I can eat them all, so the proper solution would be 5.
- Almondsetat 2y ago
  you can't divide the apples among 0 people and then claim to still have them, because in that case you would have divided them among 1 people
  - dmz73 2y ago
    Like everything in life, it depends... For example: Storage has 5 items that need to be processed. 5 items need to be split equaly between available processes. There are currently 0 available processes so 5 / 0 = 0 items to be processed is more correct than either 5 or Nan or infinity.
    - Almondsetat 2y ago
      Your example is quite vague (e.g. are we dealing with an integer number of items and processes?) and in general if something looks kinda like a division it doesn't mean it is exactly division. Just like in math, we have the power to simply say: if COND -> divide normally, else -> do something else.
  - postalrat 2y ago
    And that's why the answer is 0.
- askvictor 2y ago
  Paraphrasing you: "If I have five apples and were to divide them among 0 people, how many does each person get?" This sums up one approach to this problem, and can be thought of in a more intuitive manner than the limit approach. The answer could be zero. Or 1. Or 37. In fact, any number makes as much sense as the question. Which is why either an exception is raised, (or +- Inf is returned for floats, but that's just the limit approach). But perhaps it would be more fun just to return a random number on divide by zero :)

throwawaymaths 2y ago

1/0 = 0 is usually not a practical thing, it's to satisfy that the output of the division operator stays in the type and you don't want crashes (a "feature" of ponylang and gleam, e.g.). Its kind of a PL wonk thing. It's not at all a good idea for very important practical reasons as I outline in a reply to parent.

ncruces 2y ago
I don't want to handle errors after every division and division doesn't crash, both sound rather practical, though.
- AlotOfReading 2y ago
  The original purpose of defining it to be Nan/INF in floating point was exactly that. You'd do all the work and then check if it was Nan/INF at the end without having to check every intermediate result.
  - eru 2y ago
    If you want to do all the work at the end, 'exceptions' do exactly that, too.
    - davorak 2y ago
      Throwing an exception in a function normally stops the rest of the work that function would do. That is not the case when using Inf and similar > const f = (x) => [x/2, x/0] undefined > f(10) [ 5, Infinity ]
      - NBJack 2y ago
        I assert stopping immediately is much more practical. In many cases, you waste considerable amounts of processing power to reach a conclusion you often won't be able to use.

deleted 2y ago

[deleted]

jsnedjdn 2y ago

Never have I ever met anybody who would think dividing by zero yields zero O_o If anything it feels natural to yield +/-infinity

giraffe_lady 2y ago
It's not about what I think zero division yields I've taken a math class before. It's just about representation within the type system. If division can return infinities we can't safely combine division with other functions that are expecting ints and floats. Most languages throw an error instead, but there are tradeoffs there too. If you've decided not to throw an error you should at least return a usable number and zero makes more sense than -1 or 7 or a billion or whatever. You could also build the number stack from the ground up to accommodate this edge case, and make it so all arithmetic functions can handle infinities, infinitesimals and limits. I've come across a racket sublang like that but it's nearly unusable for the normal common things you want to do with numbers in code.
- ctenb 2y ago
  NaN is a valid float, so are infinities
  - giraffe_lady 2y ago
    They're valid according to a spec that doesn't mean I want one showing up when I'm trying to calculate the area of a semicircle or whatever. In the context of getting one by surprise in simple arithmetic they are approximately as bad as zero. Either way you have to decide how to handle it and there are tradeoffs of different approaches, as the article discusses. It's not about someone just being ignorant of basic math like the comment I was replying to implied.
    - morningsam 2y ago
      >In the context of getting one by surprise in simple arithmetic they are approximately as bad as zero. I don't think so, because getting 0 in a larger expression might yield a result that looks plausible, leading to hidden bugs. Inf and NaN both are good because they necessarily propagate all the way up to the end result, making it obvious that something went wrong.

JumpCrisscross 2y ago

> He thought 1/0 should be 0 rather than an error because "that's what people expect" So I saw this in action once, and it created a mess. Private company had a stupid stock dividend mechanism: every shareholder received some fraction, dependent on fundraising, of a recurring floating pool of shares, quantity dependent on operating performance. (TL; DR Capital was supposed to fundraise, management was supposed to operate. It was stupid.) One quarter, the divisor was zero for reasons I can't remember. This should have resulted in no stock dividend. Instead, the cap-table manager issued zero-share certificates to everyone. By Murphy's Law, this occured on the last quarter of the company's fiscal year. Zero-share certificates are used for one purpose: to help a shareholder prove to an authority that they no longer own any shares. Unlike normal share certificates, which are additive, a zero-share certificate doesn't add zero shares to your existing shares; it ambiguously negates them. In essence, on that day, the cap-table manager sent every shareholder a notice that looked like their shares had been cancelled. Because their system thought 1 / 0 = 0. If you're dividing by zero in a low-impact system, it really doesn't matter what you output. Zero. Infinity. Bagel. If you're doing so in a physical or financial or other high-impact system, the appropriate output is confused puppy.

deleted 2y ago

[deleted]

makr17 2y ago

I remember my junior high maths well enough, allowing division by zero is an essential step in proving that 1 == 2, which we _definitely_ don't want.