"Dedekind's language in introducing irrational numbers leaves a little to be desired. He introduces the irrational α as corresponding to the cut and defined by the cut. But he is not too clear of where α comes from. He should say that... α is no more than the cut. ...Heinrich Weber told Dedekind this, and in a letter of 1888 Dedekind replied that... α is not the cut itself but something distinct, which corresponds to the cut and brings about the cut. Likewise, while the rational numbers generate cuts, they are not the same as the cuts. He says we have the mental power to create such concepts."