## Numbers 2

Proof that there is morw irrationals than integers.

Proof:

Suppose you did make a list (assume it is only the irrationals from
0-1). Lets give the first numbers on the list,

1:0.5743857926410654136534629...

2:0.5785605674106541650460134...

3:0.1332538518354568254625486...

4:0.0000000000000000000000000...(After one trillion digits, there
is a one)

I can create a number that in not on the list.

The first digit is 0

0.

The next is the first number's 10s on the list +1. (If it is 9,
make it a 0.)

0.6

The next is the second number's 100s on the list +1.

0.68

Then, it continues.

0.684167836728460162738462868...

The number is not on the list.

How about the 383rd number?

0.684167836728460162738462868...

It can't be since the number's 383rd digit is different from t…