If X is an integer, what if we assume X=0 as it is not mentioned that X needs to have a positive integer?
will the answer still hold “C”?
The question is ambiguous if u consider x = 0. However, if “number of” refers to the cardinality then there’s still a bijection, so the answer is still C.
Quantity A) Cardinality of set of all positive integers
Quantity B) Cardinality of set of all negative integer
Each element of A can be mapped uniquely to each element of B and vice versa, so C.
The only factor of 0 (as per ETS) is 0, so the answer remains C as both quantities are equal to 0.
Where does it say this though? Can you post a screenshot? I don’t see their rationale for ever stating that?
See page 4/5 of https://www.ets.org/pdfs/gre/gre-math-review.pdf
Yeah that doesn’t say anything about:
The only factor of 0 is 0
It only says
0 is not a factor of any integer except 0
This doesn’t contradict anything because n = 0 \cdot q is never true unless n is 0 itself.
0 is a multiple of every integer
Which is basically the same as “the factors of 0 are every integer”
So i guess you just misread, and thus what u mentioned isn’t right.
OK fair enough. Even then what’s the ambiguity?
“number of…” implies that you need to have infinities as numbers, but there are ordinals, cardinals, etc. If the question has to do with cardinals, then the answer is clear because each set would have a unique cardinal number assigned to it and you can ask whether they’re equal. The general assumption, without context, is that “number of…” refers to natural numbers. Ordinal numbers are an extension of the natural numbers and those define infinites too. For this reason, different definitions would lead to different answers because there isn’t a unique concept of “number” for something like this.
OK. I know where you’re coming from, but the problem is that we’re clearly seeing people ask the “what about 0” for reasons that have nothing to do with this. That being said, we’ll adjust this one to exclude the 0 case.