/sci/ - Science & Math

Help, I am not able too figure out where this definition of q comes from (3)
The section that explains it says "let A be the set of all positive rationals p, such that p^2 < 2, likewise, let B be the set of all positive rationals p such that p^2 > 2.
It's easy to see that in A there is no number greater than every element of the set, and in B there is no number smaller than every element in the set "
Then they say that for each p we can associate a q such that : (3)
pls help