[noqc]

in between any two real numbers, there is a rational number, and vice versa.

[concordDance]

And yet somehow there are infinity times more reals than rationals...

Very hard to get your head around!

[noqc]

An fun, immediate, horrifying, consequence.

If I remove n elements from R, the remainder has n+1 connected components.

The complement of Z in R has |Z| connected components.

The complement of Q in R has |R| connected components.