How do I interpret this statement?
Given a set S containing n real numbers and a real number x, there are two numbers in S whose sum is x.
It's not clear to me what we can assume here. I'm not sure if x is necessarily in S.
My focus is on the assumption. I guess there are two possible interpretations:
1) $S = \{n_0, n_1, n_2, ...,n_n \}$ where $n \in \Re$, and $\exists x \in \Re$
or
2) $S = \{n_0, n_1, n_2, ...,n_n, x \}$ where $n, x \in \Re$
Basically, is $x \in S$?
If x was an element of S, it should be stated like "Given a set S containing n real numbers with a real number x being one of them" or "Given a set S containing n real numbers and a real number x in S"
Are you sure no further context is provided in the text?