Cantor’s Diagonal Argument (CDA) results is a primary controversial theorem as it was either criticized or rejected by several prominent Mathematicians amongst: Leopold Kronecker, Henri Poincaré, Ludwig Wittgenstein and Luitzen E. J. B. Brouwer.
Although Cantor teaming with Hilbert have apparently won the last battle, the opposition to CDA has never stopped, but it is rather ignored.
I use here Critical Analytical Mathematics to refute Cantor’s Diagonal Argument using the identity map. The identity map being bijective can be a reference theorem (non controversial) with higher truth to challenge a controversial theorem such as CDA.
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