in the way mat Cantor\'s Diagonalization Method Cantor published his discovery t
ID: 3111681 • Letter: I
Question
in the way mat Cantor's Diagonalization Method Cantor published his discovery that R is uncountable in 1874. Although it is actually quite similar to the one Cantor originally found. In 1891, Cantor offered another proof of this same fact that is startling in its simplicity. It relies on decimal representations for real numbers, which we will accept and use without any formal definitions. has some modern polish on it, the argument presented in Theorem 1.5.6 (i) Theorem 1.6.1. The open interval (0,1) uncountable {x E R : 0Explanation / Answer
A) The real number x is not f(1) as there are many forms of f(1) depending on am,n . But f being one one cannot map single element to multiple .
B) similarly x cannot be same as f(2) or f(3) or ..... f(n) .
C) the contradiction arises on the injectiveness or one one correspondance of the map f . Now as there is no one one correspondance between Set of natural numbers and (0,1) , hence it is uncountable
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