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…