I’m by no means a mathematician so this is a layman’s confusion after watching Youtube videos.
I understand why the (new) real number couldn’t be at any position (i.e. if it were, its [integer index] digit would be different, so it contradicts the assumption). But how does this **prove** that the set of real numbers is larger? This number indeed couldn’t be at any position, but it can **still** be mapped to an integer, because there are infinite integers – neither set can be larger because neither is finite.
Or are just “larger” or there being “more real numbers than integers” wrong terms to describe cardinality?
Pardon my ignorance.
Thank you.
In: Mathematics
there are infinities that are larger than other infinities.
To find out if two infinite sets are the same “infinity”, you need to come up with a 1-to-1 correspondence. if you can’t (and that is Cantors prove) the other infinity is larger.
Not a mathematician myself, but the concept is not that difficult.
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