Question

prove that the set of real numbers 'R' is uncountable.

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Answer 1

Answer:

The set of real numbers R is not countable. We will show that the set of reals in the interval (0, 1) is not countable.

For the first number, I’ll take the first digit; and change it to 2 if it’s 1, else to to. For the second number, I’ll do the same for the second digit; etc …

so, in the example, my number is

0.000… → first digit is 0 → 0.1

0.215… → second digit is 1 → 0.12

0.548… → thrid digit is 8 → 0.121

so the number I’m talking about is 0.121 … That real number is not on your list. Because if it were, it would be the Nth number. Yet, considering how we made our magic number, the Nth digit of this number differs with the Nth digit of the Nth number. so it can’t be that number.

Step-by-step explanation: