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
> This number indeed couldn’t be at any position, but it can still be mapped to an integer
That’s a contradictory statement. If the number can be mapped to an integer, that integer indicates its position, but you’ve said the number can’t be at any position. Mapping to an integer and having a position in the list are equivalent things. Either you have both or you have neither.
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