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This thought can be made much more concrete when talking about sets. Clearly we can understand a collection of things as a set. Clearly numbers are things, so w
by Gehinnn 6y ago
This thought can be made much more concrete when talking about sets.
Clearly we can understand a collection of things as a set. Clearly numbers are things, so we can talk about the set of all numbers. But how many elements are in this set?
A clever answer could be: It has as many elements as there are natural numbers!
As subsets are also a thing, we could ask next how many subsets the set of all numbers has.
A clever, but very problematic answer could be "as many as there are natural numbers!"
- empath75 6y agoThat’s actually not true, the power set of the naturals is uncountable.
- Gehinnn 6y agoAs I said, it would be a very problematic answer. But only if you properly define when two non-finite sets have the same size, you can lead this to a contradiction. Infinity can be understood intuitively, extending it to the cardinal numbers not.