RCDA3: this article is the third installment of a series titled ’Refuting Cantor’s Diagonal Argument (RCDA)’ In RCDA1, I propose to use formal acceptance to Cantor’s Diagonal Argument,in the second I have applied a Double Cantor Diagonal Argument refuting Cantor’s Transfinite sets In this RCDA3 article I apply formal acceptance, as suggested in RCDA1, to perform a basic sanity check to Cantor’s Diagonal Argument using the identity map between the interval [0, 1) of real numbers and itself, CDA gives the usual non surjective results, which can not apply for bijective identity map. CDA’s failure to detect a bijection ensured by the identity map proves CDA is not a valid argument to qualify a one-to-one mapping between an arbitrary set E and the real numbers interval [0, 1).
There are obviously dramatic implications for transfinite numbers, which can not be discussed in this short article. . .
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