How do you know this is real?
\((a)\) Each point on the real line corresponds to a unique real number.
\((b)\) There are more real numbers between any two consecutive integers than the whole set of Integers.
\((c)\) We can't talk about \((b)\) above, since we can't compare two infinities.
\((d)\) Every bounded interval is a finite set.
\((e)\) Some bounded intervals are finite sets.
\((f)\) There are finite irrational numbers between any two given irrational numbers.