Question

This is a very innovative proof i found. Anybody care to try it?
prove that the set of integers,thats an infinite set is smaller than the set of real numbers, that too is an infinite set

Answer 1

Nobody..?? :(

Answer 2

like a think about this


- what mean set of real numbers ?

- and what mean set of integers ?

hope this will be a good idea for begining ...

Answer 3

both are infinite sets...how do you prove one is larger?

Answer 4

@ganeshie8

Answer 5

The "size" of the infinite set isn't relevant here, though, is it? You're specifically asking if the set of integers is infinite.

Answer 6

Anyway, you can show it's infinite by showing there's a one-to-one mapping to a proper subset of itself, say the natural numbers. A diagonal argument could follow from there.

Answer 7

No integer is an irrational number.

There is a for every integer there is a real number. But the real numbers include an irrational number. Since all the integers are paired with real numbers, there is no integer left to pair with the irrational number. Therefore, there are more reals than integers.

However, you can prove that the integers and the rationals are the same size.

Answer 8

@LarsEighner thank you , so you have wrote above exactly what i have thought