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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.
Q.E.D.
