A proof of the Injectivity of the Continum Function

In this paper we prove that Two sets are isoplethic if and only if their power sets are isoplethic,(where isoplethic means that they have equal cardinalities) which is an old question in cardinalarithmetic and is called ICF(Injective ContinuumFunction). It is known to follow from GCH( Generalized continuum hypothesis).On this paper weprove ICF without assuming GCH or anything controversial by applying the Erdos Kaplansky Theorem which asserts that the dimension of the dual of a infinite dimensional vector space over any fieldis equal to the the cardinality of the dual.To be more specific we show that ZFC implies ICF. Finally byapplying ICF and invoking the celebrated 1964 paper of Paul Cohen, which together with his 1963paper implied the independence of CH from ZFC, we prove that Set Theory ZFC is inconsistent(if the paper of Cohen is valid