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. Such as by 10, 25, 38, and so on.

 

[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.

 

[FactChecker]

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.

That is where "infinity" begins. It is the size of the smallest infinite set. It's size is denoted by $\aleph_0$. There are larger infinite sets of size $\aleph_1$, $\aleph_2$, ... etc.

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.

Yes.

What does this mean/imply?

Good question. The subject is interesting. You might be interested in the work of Georg Cantor in the late 1800s. He formalized the study of "infinity" and proved that there were sets with sizes larger than the size of the set of natural numbers.