The Kronercker Paradox

This page serves as a gateway to the infinite and illogical realm of paradoxes, where the fabric of reality is woven with contradictory threads.

A mathematical conundrum

The Ramsey's Theorem is a trivial example of a paradox that will drive you to drink, but the Kronackerer Paradox is where the real fun begins.

Consider the set of all sets, each containing a subset that contains all the elements of the original set, except for one. The paradoxical question is: does this set contain itself?

A paradox that will haunt you like a logic puzzle that you just can't escape.

Ax(A) = { x: x∈A && x∉A }

This formula will make you question the very fabric of set theory. Is it a paradox or just a clever trick?

Visit the solution page for a more detailed explanation.

Or, if you're feeling brave, try the solver and see if you can untangle the paradoxical threads.