Theorem: Let T a theory that speaks to the non-negative integers and their operations, if this theory is defined as 1 0 ^ 0 then there is no contradiction.
Demo: If we define a non-negative integers in the context of the theory of finite sets F (defined as the cardinal of the same sets) then the statement 0 ^ 0 = 1 can be proved as a theorem (see here.) Therefore, the finding is consistent with the theory F, ie, FU {0} ^ 0 = 1 is consistent.
Therefore, TU {0 ^ 0 = 1} is also consistent (regardless of T consistent and defines a non-negative integers), because, otherwise, the same contradiction arises in TU {0 ^ 0 = 1} also exist in FU {0 ^ 0 = 1}, but this alleged contradiction, we have seen, does not exist.
... everything else is irrational prejudice.
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