8 ms·

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 bas

by ilius2 2y ago

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?

ilius2 2y ago
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.
- sidpatil 2y ago
  What if a is negative?
  - ilius2 2y ago
    Same. Unless you want to differentiate -0 and +0 (which make it more complicated), you can not distinguish infinity from negative infinity.
    - jsnedjdn 2y ago
      IEEE floating point representation does both
    - HappMacDonald 2y ago
      John Conway can
clipsy 2y ago
> 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.
- ilius2 2y ago
  Yes, I meant when the result gets bigger. You get the idea.
  - ncruces 2y ago
    What's the output of this Go program, without going to the playground link? print(math.MinInt / -1) https://go.dev/play/p/Vy1kj0dEsqP https://go.dev/play/p/Vy1kj0dEsqP
scarmig 2y ago
Floats don't have multiplicative inverses, and the floating point operations don't give us any of the mathematical structures we expect of numbers. Floating point division already abandons algebra for the sake of usefulness.
- mjcohen 2y ago
  Knuth vol 2 has a nice discussion of floating point operations and shows how to reason about them. Wilkinson's classic "Rounding Errors in Algebraic Processes" (1966) also has a good discussion.

by ilius2 2y ago

ilius2 2y ago

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.

sidpatil 2y ago
What if a is negative?
- ilius2 2y ago
  Same. Unless you want to differentiate -0 and +0 (which make it more complicated), you can not distinguish infinity from negative infinity.
  - jsnedjdn 2y ago
    IEEE floating point representation does both
  - HappMacDonald 2y ago
    John Conway can

clipsy 2y ago

> 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.

ilius2 2y ago
Yes, I meant when the result gets bigger. You get the idea.
- ncruces 2y ago
  What's the output of this Go program, without going to the playground link? print(math.MinInt / -1) https://go.dev/play/p/Vy1kj0dEsqP https://go.dev/play/p/Vy1kj0dEsqP

scarmig 2y ago

Floats don't have multiplicative inverses, and the floating point operations don't give us any of the mathematical structures we expect of numbers. Floating point division already abandons algebra for the sake of usefulness.

mjcohen 2y ago
Knuth vol 2 has a nice discussion of floating point operations and shows how to reason about them. Wilkinson's classic "Rounding Errors in Algebraic Processes" (1966) also has a good discussion.