minus-square@[email protected]linkfedilink2•2 days agoA 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.
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.