A set of propositional formulas is satisfiable if and only if all finite subsets of it are satisfiable.

The cardinality of a set is always smaller than the cardinality of the set of subsets of the former set.

A set cannot contain itself.

There is no 1 to 1 mapping from the natural numbers to the real numbers.

There is a 1 to 1 mapping from the natural numbers to the rational numbers.

Something exists. I cannot tell you what it is but it does exist. Maybe reality is an illusion but even then the illusion exists.