No.14427894 ViewReplyOriginalReport
>Let set A = { a, b, c, … }
set B = {1, 2, 3, … }

>These 2 sets have the same cardinality as there exists a bijection between the two.

>Now let’s introduce the set C = {0, 1, 2, 3, …}.

>It also has the same cardinality as set A.

>Now let’s create a mapping between sets B and C, such that if x > 0, x ~ x.

>This mapping is not surjective, since there is no member in B such that 0 can be mapped to. Therefore the mapping isn’t bijective and these two sets are not equal, which is a contradiction, as two things equal to another must be equal to themselves.

>Therefore modern mathematics with its notion of infinite sets is retarded.