How does cardinality apply to real numbers?

Tau

Jan 2014
86
4
Isn't cardinality a concept that concerns discrete quantities? How then can you talk about the cardinality of real numbers which are continuous?
 

mathbalarka

Math Team
Mar 2012
3,871
86
India, West Bengal
Tau said:
Isn't cardinality a concept that concerns discrete quantities?
No, in general. True if 'cardinality' is replaced by 'countable cardinality'.
 

Tau

Jan 2014
86
4
Thanks for the replies. So, my problem is understanding the definition of cardinality of uncountable infinity/ continuum. So, my question is how does that follow from ZFC axioms? Or if it's a new definition what's the proof that it's consistent with ZFC.