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Suppose I have a set of values for x: something like {1, 2} and another set for y: {3,4}. If I need to list all the possible points which coordinates are permutations of those sets and I don't want to list them explicitly, how would I do it? Best I can do is P(x,y):{x$\in${1,2}, y$\in${3,4}}, but I think it's wrong. How should it be notated correctly?

PupaLupa
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  • You seem to be using words incorrectly. Are you able to explicitly write out the result of the operation without set builder notation? Are you perhaps looking for ${(1,3),(1,4),(2,3),(2,4)}$? How do "permutations" come into this? – JMoravitz May 26 '20 at 19:06
  • @JMoravitz , you are right. Sorry, I'm still figuring out all the names, but the closest concept I know is permutations, so I called it permutation :) By 'explicitly' I mean writing down all points like P(1, 3), P(1, 4), P(2, 3), P(2, 4). – PupaLupa May 26 '20 at 19:17
  • I don't believe you should be including these $P$'s in what you write either. I suppose it isn't explicitly wrong... but certainly confusing, cluttering, and unnecessary. It is perfectly acceptable to refer to "the point $(1,3)$." – JMoravitz May 26 '20 at 19:20
  • @JMoravitz I just solved a problem where the answer is a set of 9 points, so I figured it would be much prettier to use some sort of notation. Can I give an answer in a form like: X= {some values} and Y={some other values} Answer : Point (x, y): (x, y)$\in$X×Y or it is nonsense? – PupaLupa May 26 '20 at 19:31
  • "where the answer is a set of 9 points" So then, your answer can be $X\times Y$. No need to talk about ${(x,y)~:~(x,y)\in X\times Y}$, that is redundant. – JMoravitz May 26 '20 at 19:43
  • @JMoravitz understood, many thanks for you answer – PupaLupa May 26 '20 at 20:03

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Say $X=\left\{1,2\right\}$ and $Y=\left\{3,4\right\}$, you're looking for the cartesian product: $$X\times Y=\left\{(x,y):x \in X, y\in Y\right\}=\left\{(1,3),(1,4),(2,3),(2,4)\right\}.$$

Thomas Markov
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