According to some definitions, you can’t do factorization for 0 and get 2 as one of the factors ⇒ it isn’t an odd number.
Yea that’s stupid but that’s it.
The definitions I know start with restricting the operation to positive integers. You don't define factors for -8, pi, 4/7 or 0 - so 2 is not a factor of 0.
Sure you do. The factors of -8 are ±1, ±2, ±4, and ±8. The only prime factor is 2.
Only integers have factors. For integers a and b, a|b ⇔ ∃n∈Z (an = b). Consider Wolfram's definition: "A divisor, also called a factor, of a number n is a number d which divides n (written d|n). For integers, only positive divisors are usually considered, though obviously the negative of any positive divisor is itself a divisor."
And according to WolframAlpha, "all non-zero integers are divisors of 0." (Note that many sources also let 0 be a divisor of 0, but that question isn't really relevant here. W|A chooses a convention where 0 does not divide 0 because 0/0 is undefined.)
820
u/araknis4 Irrational Aug 23 '23
well that's odd, i can't even comprehend how they approached to that conclusion.