[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.

[pasquinelli]

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