Practice question · True or false
Cantor’s theorem shows there is no largest infinite set.
Hints
- The theorem compares a set with its own power set.
- Since the power set is always strictly larger, the process never terminates.
Show the answer
True
Why
True, the power set of any set is strictly larger, so no set can be maximal. Applying the theorem repeatedly generates an endless hierarchy of infinities, which is where set theory stops being bookkeeping.
Practise Relations, Functions and Power Sets
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