Given the following list of real numbers, use Cantors technique to create a number that is not

Fantastic news! We've Found the answer you've been seeking!

Question:

Given the following list of real numbers, use Cantor’s technique to create a number that is not in the list:

Real Numbers

1 0.123456789101112131415161718...

2 0.246810121411618202224262830...

3 0.369121518212427303336394245…

4 0.481216202428323640444852560…

5 0.510152025303540455055606570…

Instructions

Why will this process create a number that is guaranteed to be different than all of the numbers on a list that is infinitely long?

Why will this process create a new number for ANY list?

In Cantor’s argument, is it possible to consider pairs of digits rather than single digits? I.e. To build M, suppose we look at the first two digits of the first real number of our list. If they are not 22, make them 22; if they are 22 make them 44. Repeat this process. Will the resulting number M be unique, and not a member of the original list.