1/0 is infinity but 1/(-0) is -infinity
The same goes for the floating-point infinity: it doesn't represent the concept of infinity, it is a placeholder for every number between the largest representable number and infinity. That's how dividing a very large number by a very small number can result in infinity, a number which is really not a number.
This is the philosophy by which IEEE floating-point numbers were designed, and it's the explanation behind which negative zeroes and infinities make sense in floating point.
The way I find it easiest to reason about is by taking a graph of an asymptote and rounding it to the nearest units. You somehow need a way to say "there is an asymptote here!" even though you might not have all the units, and so you introduce infinities and negative zeroes to maintain as much precision as possible.
Totally NOT. NaN is defined as 0.0/0.0. That's it.
For instance:
- as parent said 1/0 is Inf.
- as parent said 1/(-0) and log(0) is -Inf.
- sqrt(-1) and 0/0 is NaN.
[1] https://www.gnu.org/software/libc/manual/html_node/Infinity-...
what we have is lim(x->0+) 1/x = +inf and lim(x->0-) 1/x = -inf
however, it is irrelevant to the fact that a commenter was disagreeing because they had confused ieee-754 division with the division operation on so-called 'real' numbers
"There are mathematical structures in which [dividing by zero] is defined. [...] However, such structures do not satisfy every ordinary rule of arithmetic (the field axioms)." https://wikipedia.org/wiki/Division_by_zero
You're familiar with the ordinary rules of arithmetic (ORA!) applied to the real numbers. However, there are many number systems that follow different rules.
The rules of arithmetic for floats, wraparound ints, elliptic curves, and asymptotic analysis are all different from ORA! (and each other) but they are useful in their own ways.
That's not at all true. The inclusion of negative zero in ieee 754 was a deliberate design choice, and if it were considered desirable that zero should be unsigned, then the bit pattern assigned to -0 would not have been so designed. See 'much ado about nothing's sign bit'[0], by one of the principal authors of ieee 754.
Whereas -0 and +0 are not operationally equivalent, operational equivalence is an important and useful relation; see the very pattern matching example linked from the OP[1].
=:= (=== in elixir) Somewhat means "and has the same binary form"
Fwiw, julia made the exact same choices.
This is actually a valid distinction because these values can represent different values.
Floating point values are not numbers, but ranges of possible values: float -0 is a number in the range (-FLT_TRUE_MIN / 2, 0] and float +0 is a number in the range [0, FLT_TRUE_MIN).
IMO if I were to redesign IEEE 754 I would add a third float 0 value that always represents exactly 0 and redefine float -0 and float +0 as open limits, but that would probably make everything a lot more complicated.