As other users mentioned, the most relevant part is when you divide by 0, you get different infinities depending on if you're dividing by +0.0 or -0.0. But even beyond that: the binary representation of floating point numbers [1] necessarily means that there are two values for zero with distinct bit patterns.

Floating point numbers have a dedicated sign bit that specifies the sign, which means that you can flip the sign of any floating point number and get a float with a different bit pattern (and opposite sign). That means that you get necessarily get both +0.0 and -0.0, and they have different internal representation in bits.

This is one of the major advantages of two's complement notation for representing integers: it doesn't have a dedicated sign bit in the same way, so you only get one representation for 0. You can still check the sign by looking at the top bit, but if you flip it for the number 0, you don't get -0 (which doesn't really exist), you get -128 (for 8 bit signed integers).

[1]: https://en.wikipedia.org/wiki/Double-precision_floating-poin...

They are distinct values but they compare equal. For almost all uses they are effectively equal, except where you are producing infinities.