[divides_by_zero]

But now you're changing your proof. Just because the number of hot chicks and non hot chicks can be put into bijective correspondence with a countable number of hot chicks doesn't magically change the ugly chicks into hot chicks.

The rationals can be put into bijective correspondence with the integers. However, even though you can put them into 1-1 correspondence 1/2 is still NOT AN INTEGER.

You need an isomorphism and all you have is a bijective map.