Countable infinity is uncountable infinity

If we write all the numbers big-endian, like 0,1,2,3,4,5,6,7,8,9,01,11,21... then put a decimal point before it and put all the numbers before that, like 0.0, 0.1, 0.2... 0.01, 0.11.. 1.0, 1.1... then since infinity squared is still infinity cus infinity is endless, that means that uncountable infinity IS countable infinity.

0 - 0, 0.1, 0.2, 0.3 ... 0.9, 0.01 ...
1 - 1, 1.1, 1.2, 1.3 ... 1.9, 1.01 ...
...

disproof

there are uncountably many irrational/trancendental numbers. 10-adic numbers repeat.