- #1
jostpuur
- 2,116
- 19
How do you prove that if [itex]\textrm{card}(X)\leq\textrm{card}(Y)[/itex] is not true, then [itex]\textrm{card}(X)\geq\textrm{card}(Y)[/itex] must be true?
In other words, if we know that no injection [itex]X\to Y[/itex] exists, how do we prove that an injection [itex]Y\to X[/itex] must exist?
This is not the same thing as what Cantor-Bernstein-Schroeder theorem answers, right?
In other words, if we know that no injection [itex]X\to Y[/itex] exists, how do we prove that an injection [itex]Y\to X[/itex] must exist?
This is not the same thing as what Cantor-Bernstein-Schroeder theorem answers, right?