[v4vvdq]

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.

[eqvinox]

In IEEE 754 math, x/0 for x < 0 is in fact negative infinity.

  >>> 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.

[numpad0]

I always thought the answer to verbal query "let y=1/x, x=0, find y" was "Well, the answer is the Y axis of the plot". Surprising that people have to be reminded that X can be signed. I've had similar conversation IRL.

[ConspiracyFact]

You seem to have your axes confused. The value of y can’t be “the y-axis”, which is the line x = 0 (for all values of y).

[WithinReason]

on computers you can have negative zeros

[recursive]

Negative zero is equal to zero, so it's not really a distinct number, just another representation of the same value.

[epidemian]

It's equal (as in, comparing them with == is true), but they are not the same value. At least in IEEE 754 floats, which is what most languages with floating point numbers use. E.g., in JS:

  > 1 / 0
  Infinity
  > 1 / -0
  -Infinity
  > 0 === -0
  true
  > Object.is(0, -0)
  false

[recursive]

I think you're misunderstanding me. They are the same value, but a different representation. The equivalence of the value can be shown with math, and has nothing to do with the implementation details of IEEE 754.

[eru]

Yes.

In a language like C or Rust, you can cast your +0.0 and -0.0 to an integer, and print out the bit pattern. They are different.

[atsmyles]

-0 is a notation for 1 / -infinity, so it is distinct. For addition it is not.

[pasquinelli]

that's really just an encoding of the number to help you understand how the hell you got here