Linked from
The 87 pages that link to Real number, each with the reason it gives.
Set theoryBroader topic: Set constructions provide rigorous models of the real numbers.
FieldBroader topic: The real numbers provide the standard field for continuous mathematics.
Uncountable setBroader topic: The real numbers are the standard example of an uncountable set.
Cantor–Dedekind axiomBroader topic: These are the numerical values assigned to line points.