Hi, I am a lowly intruder who knows nearly nothing about mathematics. I hail from English Language and Usage with some questions regarding regarding the word vinculum I think you folk might know better than my peers: First would you please tell me if any of you would recognize the word vinculum offhand? Also, if you can recognize it, would you also give me a personal opinion as to whether it can be used as a synonym for fraction bar, or if it is restricted to binding the order of operations?
If you have $f : X \to Y$, then $f$ typically does not consist of all pairs $(x,y)$ where $x \in X, y \in Y$ (that would be $X \times Y$), it consists of all pairs $(x,y)$ for which $f(x) = y$.
Hmm, the reason I'm asking is because I am getting some conflicting data from different sources. I'm not sure if I know any better now than I did before but I think your opinions will be helpful for my purpose regardless. Thank you @MeesdeVries and @AkivaWeinberger .
@Tonepoet, for what it's worth, at least two mathematicians do not know the word, so stay away from it in text that is supposed to be easy to understand, if you can.
@Mahmoud, sure, if you want. But really, in formal ZFC, $f(x) = y$ is just a shorthand for $(x,y) \in f$, so this is pretty trivial. Also, you can make the vertical bar in your set builder notation with \mid.
