Why are positive rational numbers countable but real numbers are not?
6681
How does Cantor's diagonal argument work?
18360
Proof that the irrational numbers are uncountable
102543
Real definition of "countable set"
68139
Show that the set of polynomials with rational coefficients is countable.
157733
Are positive real numbers $x,y$ allowed to be taken out during this proof?
85895
Proving all rational numbers including negatives are countable
8061
Why must the base of a logarithm be a positive real number not equal to 1?
78294
How does one denote the set of  all positive real numbers?
116135
A paradox related to computable reals?
120935
Why is every continuous function on the reals determined by its value on rationals?
3645
Why Are the Reals Uncountable?
135815
Why isn't there a uniform probability distribution over the positive real numbers?
22391
Is the set of all pairs of real numbers uncountable?
119545
Nonzero rationals under multiplication are not a cyclic group
86685
Example of a set $S$ that is countable, but the set of limit points is uncountable
34710
Cardinality of Irrational Numbers
114650
In Cantor's Diagonalization Argument, why are you allowed to assume you have a bijection from naturals to rationals but not from naturals to reals?