(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Using the Schroeder-Bernstein Theorem, prove the following sets must have the same cardinality by producing explicit one-to-one (but not necessarily surjective) maps f: A-->B and g: B-->A.

(a) The unit disc in the plane A={(x,y) in R2: x^2 + y^2 <1} and the unit square B={(x,y) in R2: x,y in [-1,1]}.

(b) The unit disc in the plane A={(x,y) in R2: x^2 + y^2 <1} and the entire plane B=R2.

3. The attempt at a solution

I'm having trouble with this section we're working on because I don't know how to come up with an injective function at the top of my head.

For (a) the map g, can I use the map (x,y)-->(x^2 + y^2)/2?

For (b) the map g, can I use the map (x,y)-->(x^2+y^2)/(x^2+y^2)+1???

You can probably tell I am lost.

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# Homework Help: Prove sets are equipotent using Schroder - Bernstein

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