What does it mean to have one-to-one correspondence between infinite sets. How would you solve them?
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$\begingroup$Here's an example. Consider the set $A=\{\,1,2,3,4,\dots\,\}$ of positive integers and the set $B=\{\,2,4,6,8,\dots\,\}$ of positive even integers. The function $f:A\to B$ given by $f(x)=2x$ is a one-to-one correspondence between these two infinite sets, because 1) it is a function from the one to the other, 2) no two different things in $A$ get mapped to the same thing in $B$, and 3) nothing in $B$ gets left out.
I don't know what you mean by "how would you solve them?" One solves equations, one doesn't solve correspondences.
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