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СпутникиРНSpaceXРоскосмосNASAWhat 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.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?
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.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.
Yes.
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.
I don't know that it means anything. It's just an interesting fact. That's what "pure mathematics" is all about. If you make any reference to meaning they don't like it. They want no reference to the real world contaminating their math.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?
You probably want to say it is a (?? thing ??) that is greater than any natural number. But what is (?? thing ??)? What are its other properties?
Cantor's formal study of "infinity" involves mappings between sets in addition to plain set theory.
IMHO, this discussion can not make progress until you show that you have at least read about Cantor's approach.
Results of arithmetic operations to natural number except division by 0 which is not defined belong to 0 and plus-minus rational number
$$\pm\frac{n}{m}$$
whose cardinal is same with natural number.
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