The natural numbers and logical consequences of them

[mr3000]

TL;DR

The definition of infinity is that it is how many natural numbers there are. You can take those infinite natural numbers and slice them into an infinite number of infinite sets, each of which can then be sliced the same way ad infinitum.

The definition of infinity is that it is how many natural numbers there are. You can take those infinite natural numbers and slice them into an infinite number of infinite sets, each of which can then be sliced the same way ad infinitum.

What does this mean/imply?

 

[anuttarasammyak]

What do you mean by slicing numbers? Could you give us some examples?

 

[mr3000]

Dividing them.

 

[PeroK]

The definition of infinity is that it is how many natural numbers there are. You can take those infinite natural numbers and slice them into an infinite number of infinite sets, each of which can then be sliced the same way ad infinitum.

What does this mean/imply?

The natural numbers form a countably infinite set. You can partition the natural numbers into a finite collection of infinite sets. E.g. into odd and even numbers. Or, into sets depending on the remainder when divided by 10.

But, you can't partition them into an infinite collection of infinite sets. That would require an uncountable infinity, such as the real numbers.