Why is this so:
1 === 1;// true
0 === -0;// true
1/0 === 1/-0;// false
Reason:
1/0=Infinite;
1/-0=-Infinite;
Question:
Why isn't 1/0 or 1/-0 Undefined or NaN?
It can't be Infinity or -Infinity, because of 0 is equal to -0, so 1/0 is equal to 1/-0 I should say, but why it isn't? And why it isn't Undefined (what my calculator says) or NaN.
This is because the IEEE 754 specifications define it like that.
There is however a reasoning for this: the affinely extended real number system extends the real numbers with the two infinities, which gives some more room for calculating with limits. So with this extension a division by zero is not undefined or NaN.
Consider that the following is true for positive x:
limx→0(x) = limx→0(-x)
However the following is not true for positive x:
limx→0(1/x) = limx→0(1/-x)
Note how the above comparisons with limit notation map to the comparisons you listed:
0 === -0;// true
1/0 === 1/-0;// false
Secondly, a division always maintains the following invariance: the result is negative if and only when exactly one of the operands is negative.
Both of these considerations give some credence as to why in IEEE 754:
1/0 === Infinity
1/-0 === -Infinity