Note that the ONLY assertion being made in the original problem formulation is that the two envelopes contain x and x/2 with EQUAL probability. But because an absurdity follows from this - namely that it is profitable to continually keep switching envelopes - the assertion itself must therefore be false.

Note that the ONLY assertion being made in the original problem formulation is that the two envelopes contain x and x/2 with EQUAL probability. But because an absurdity follows from this - namely that it is profitable to continually keep switching envelopes - the assertion itself must therefore be false.