If aleph-null socks are lost in the laundry, how many pairs of socks does John have?.    From Wordnik.com.  [The candidate's a dodger, a well-known dodger] Reference

This last designation he applied to whatever cardinal number comes next in order after aleph-null; its identity with C, the number of real numbers or "power of the continuum," is a famous conjecture of Cantor's, his "continuum hypothesis.".    From Wordnik.com.  [An Infinity of Points] Reference

Both sets have a count or cardinality equal to the transfinite number ‎ א ‎ ‪ 0 - aleph-null.    From Wordnik.com.  [TierneyLab] Reference

As for the aleph-null and aleph-one: it was proven that the continuum hypothesis essentially whether the cardinality of real numbers is aleph-one or higher is undecidable in standard set theory, so whether you want to accept it or not, you won’t hit any contradictions.    From Wordnik.com.  [Intelligent Design explained: Part 2 random search - The Panda's Thumb] Reference