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## Homework Statement

Let S be the set of all functions mapping the set {√2, √3, √5,√7} into Q. What is the cardinality of S?

## Homework Equations

## The Attempt at a Solution

I have been stuck staring and trying to think of something to figure out this question. This is the idea i have:

let U = { all irrational numbers} V = {√2, √3, √5,√7}. Define a set T = {g: U--> Q} Now I think it might be easier for me to get the cardinality of T and since S would be a subset of that then perhaps go from there?

Now looking at it again I don't think it's as swell of an idea. But it's the only thing I got to try. With that, I'm still stuck in tyring to associate T with a cardinality I know (in this case I think it's going to be associated to the cardinality of Q).

Do I have to come up with a specific bijective function that would work?

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