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1/0 = 0 (2018)

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Re: 1/0 = 0 (2018)

#41

Post by thaumasiotes »

TrianguloY wrote: post #33

I've always wondered what would happen if we defined /0 as a new symbol, for example 'z'. The same as we define sqrt(-1) as 'i'. So if you can do 4*sqrt(-1)=4i, you could also do 4/0 = 4z. These two seems similar, as in taking something that should not exist, and just letting it exists in a totally different and orthogonal domain. I tried once to investigate the implications, but it quickly became far more complex th…

It's just a waste of time. The reason no value is conventionally assigned for division by zero is that assigning a consistent value doesn't help. When you want a value for that kind of expression at all, you'll want different values in different expressions.

Re: 1/0 = 0 (2018)

#42

Post by _Sycamore »

My head-canon with dividing by zero is that 1/0 = undefined and 1/-0 = -undefined, and that's where I leave it because anything less funny than that seems like an impractical answer.

Re: 1/0 = 0 (2018)

#43

Post by thaumasiotes »

Asooka wrote: post #35
d_tr wrote: post #30

Whatever as long as the name does not imply that these are integers, because then it is just wrong. The same holds for overflowing results being clamped or resulting in smaller or negative values due to wraparound. These are not integers. There is only one correct behavior for something named "int". Give the correct result or throw an error.

Those are all integers. https://en.wikipedia.org/wiki/Modular_arithmetic - "The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801." They have been integers for over 200 years now.

Wrapping around is correct integer behavior; clamping ("5 + 1 = 5") isn't. Clamping implies immediately that all positive numbers are equal to zero.

Re: 1/0 = 0 (2018)

#44

Post by riwsky »

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.

Re: 1/0 = 0 (2018)

#45

Post by maxk42 »

_Sycamore wrote: post #42

My head-canon with dividing by zero is that 1/0 = undefined and 1/-0 = -undefined, and that's where I leave it because anything less funny than that seems like an impractical answer.

0 / 0 = Any number

non-zero / 0 = No number

Re: 1/0 = 0 (2018)

#47

Post by thaumasiotes »

recursive wrote: post #27
lupire wrote: post #14

Earlier quoted context omitted.

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 comp…

> 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.

Re: 1/0 = 0 (2018)

#48

Post by ilius2 »

tux3 wrote: post #26
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.

Reusing symbols like +, *, or / to define operations that aren't the + or the / you're used to is pretty common in math. It's just notation. At the end of the day, the / that we have in programming has the same problem as this article's /, almost all programming languages will return 5/2 = 2 when dividing integers, even though 2 * 2 is not 5! Division is not defined for all integers, but it's just convenient to exten…

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 bother having any numbers at all?

Re: 1/0 = 0 (2018)

#49

Post by alganet »

TrianguloY wrote: post #33

I've always wondered what would happen if we defined /0 as a new symbol, for example 'z'. The same as we define sqrt(-1) as 'i'. So if you can do 4*sqrt(-1)=4i, you could also do 4/0 = 4z. These two seems similar, as in taking something that should not exist, and just letting it exists in a totally different and orthogonal domain. I tried once to investigate the implications, but it quickly became far more complex th…

In SQL, if you divide by zero, you get a NULL. If you divide by NULL, you get NULL (any operation involving a NULL yields NULL, even GROUP BY). I call it "a black hole zero", if it touches anything, that thing becomes a black hole zero.

Some languages will wrap division by zero in a special type, a NaN (not a number). You can then reason on top if that NaN if you want to.

So, in a sense, there are some people already doing practical stuff with substituting /0 for a new symbol.

Re: 1/0 = 0 (2018)

#50

Post by ilius2 »

ilius2 wrote: post #48
tux3 wrote: post #26

Earlier quoted context omitted.

Reusing symbols like +, *, or / to define operations that aren't the + or the / you're used to is pretty common in math. It's just notation. At the end of the day, the / that we have in programming has the same problem as this article's /, almost all programming languages will return 5/2 = 2 when dividing integers, even though 2 * 2 is not 5! Division is not defined for all integers, but it's just convenient to exten…

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…

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.
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