3 ms·

x div 0 = infinity, which is inconvenient if not impossible to represent in most numerical systems and makes for pernicious frame lag in video games. when we f

x div 0 = infinity, which is inconvenient if not impossible to represent in most numerical systems and makes for pernicious frame lag in video games. when we figure out how to represent the problem and state the solution in fine enough grain for accuracy we may find we have recreated the universe. i suspect no one has the patience to wait out the full run for to see the results.

sp332 3y ago
It doesn't equal infinity, it is undefined. x/n approaches infinity as n goes to 0, but at n=0 there is no answer. One way to think of it is x/n = m therefore n * m = x. You can recover the original value by multiplying the result by the denominator. But when n=0, you can't multiply 0 by anything to get x. There is just no such number.
- jacknobody 3y ago
  I think it's a matter of convention, and that all the maths I can think of survives the following definitions: If infinity were to be defined as immeasurably large, and zero as immeasurably small, we would be saying infinity=(some finite number)/0 and 0=(some finite number/infinity This still leaves us unable to find an definite answer to the multiplication of 0 and infinity, because we might have chosen any 2 finite numbers for the definitions above.
  - anankaie 3y ago
    The problem is that the "infinitely small" is already defined, and not equal to zero: The infinitesimal. It is not so simple as defining what the result should be - one needs to make sure this is consistent with the rest of mathematics, or rather, with the mathematics generated by the rest of your axioms and definitions, without resulting in paradox. If anything, division by zero generates the set of all numbers in your field. That is consistent with division being the operation of finding the multiplicative inverse, but inconsistent with the idea that arithmetic operations have only a single result, rather than a set - but this already exists in finding k-roots of numbers, so it is not completely unreasonable to treat some arithmetic operations as potentially resulting in sets. Is it a useful definition? Unclear.
magicalhippo 3y ago
In IEEE 754, division by zero is well defined[1], and some algorithms rely on this[2]. Not sure how it relates to frame lag, some less-than-ideally-implemented iterative routine? [1]: https://en.wikipedia.org/wiki/IEEE_754#Infinities https://en.wikipedia.org/wiki/IEEE_754#Infinities [2]: https://tavianator.com/2011/ray_box.html https://tavianator.com/2011/ray_box.html

sp332 3y ago

It doesn't equal infinity, it is undefined. x/n approaches infinity as n goes to 0, but at n=0 there is no answer. One way to think of it is x/n = m therefore n * m = x. You can recover the original value by multiplying the result by the denominator. But when n=0, you can't multiply 0 by anything to get x. There is just no such number.

jacknobody 3y ago
I think it's a matter of convention, and that all the maths I can think of survives the following definitions: If infinity were to be defined as immeasurably large, and zero as immeasurably small, we would be saying infinity=(some finite number)/0 and 0=(some finite number/infinity This still leaves us unable to find an definite answer to the multiplication of 0 and infinity, because we might have chosen any 2 finite numbers for the definitions above.
- anankaie 3y ago
  The problem is that the "infinitely small" is already defined, and not equal to zero: The infinitesimal. It is not so simple as defining what the result should be - one needs to make sure this is consistent with the rest of mathematics, or rather, with the mathematics generated by the rest of your axioms and definitions, without resulting in paradox. If anything, division by zero generates the set of all numbers in your field. That is consistent with division being the operation of finding the multiplicative inverse, but inconsistent with the idea that arithmetic operations have only a single result, rather than a set - but this already exists in finding k-roots of numbers, so it is not completely unreasonable to treat some arithmetic operations as potentially resulting in sets. Is it a useful definition? Unclear.

magicalhippo 3y ago

In IEEE 754, division by zero is well defined[1], and some algorithms rely on this[2]. Not sure how it relates to frame lag, some less-than-ideally-implemented iterative routine? [1]: https://en.wikipedia.org/wiki/IEEE_754#Infinities https://en.wikipedia.org/wiki/IEEE_754#Infinities [2]: https://tavianator.com/2011/ray_box.html https://tavianator.com/2011/ray_box.html