One to one correspondence between transcendental and uncomputable numbers I know that both sets are uncountable infinite but the transcendentals are not a subset of the uncomputables. I don’t know if there exist uncomputable numbers that are not transcendental. But my question is whether the two sets have the same cardinality.

Here 
https://en.wikipedia.org/wiki/Computable_number 
under "properties" it is stated the the set of computable numbers is countable. 
Hence, the set of uncountable numbers must be uncountable infinite and hence have the same cardinality as the set of transcendental numbers which is uncountable infinite as well.
