High Quality Content by WIKIPEDIA articles! Pocket set theory (PST) is an alternative set theory in which there are only two infinite cardinals. The theory is authored by American mathematician Randall M. Holmes, although the basic idea was suggested by Rudy Rucker in his Infinity and the Mind. There are at least two independent arguments in favor of a small set theory like PST. PST uses standard first-order language with identity and the binary relation symbol scriptstyle{ in }. Ordinary variables are upper case X, Y, etc. In the intended interpretation, the variables these stand for classes, and the atomic formula scriptstyle{ X in Y } means "class X is an element of class Y". A set is a class that is an element of a class. Small case variables x, y, etc. stand for sets. A proper class is a class that is not a set. Two classes are equinumerous iff a bijection exists between them. A class is infinite iff it is equinumerous with one of its proper subclasses.

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