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So what about an "infinite set"? Well, to begin with you should say precisely what the term means.
Okay if you don't, at least someone should. Putting an adjective in front of a noun does not in itself make a mathematical concept.
Cantor declared that an "infinite set" is a set which is not finite. Surely that is unsatisfactory, as Cantor no doubt suspected himself. It's like declaring that an "all-seeing Leprechaun" is a Leprechaun which can see everything. Or an unstoppable mouse is a mouse which cannot be stopped. These grammatical constructions do not create concepts, except perhaps in literary or poetic sense. It is not clear that there are any sets that are not finite, just as it's not clear that there are any Leprechauns which can see everything, or that there are mice which cannot be stopped.
Certainly in science there is no reason to suppose that "infinite sets" exist. Are there and infinite number of quarks or electrons in the universe? If physicists had to hazard a guess, I am confident that the majority would say: No. But even if there were an infinite number of electrons it's unreasonable to suppose that you can get an infinite number of them all together as a single data object
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>anime
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mathematics and the universe are two completely separate things
you can use math to build maps of the universe, but they are fundamentally different
stay in school kiddo
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>>9155886
> he's this new
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>>9155893
>all mathematical concepts represent material realities
read plato kiddo
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>>9155881
Can you let this copy pasta die?
The leprechaun analogy is flawed because infinite does not imply everything. The correct analogy would be
The all seeing leprechaun can always see at least one sight that you cannot.
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>>9155881
didn't you already realize that you have no understanding of the subject the last time you posted this thread? I don't mind you asking questions, but if people give you answers and refer you to sources then the least you can do is listen and learn a bit.
saged.
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>>9155881
>Certainly in science
Math is not a science in the sense that the other natural sciences are, so that's a pretty bad point to make. Besides there's no reason to believe that the universe is finite afaik.
Cantor's definition is alright as long as we have a correct definition for "finite" and "set". Now, it turns out that we can define what it means for a set to be finite (for example, if it cannot be put in one-to-one correspondence with one of its proper subsets) and it remains to find a correct definition for set.
Now, as it turns out, sets are a foundational concept (at least that's the way things have been done for a century) that we don't define, but for the use of which we give very precise rules (ie. the axioms of set theory)
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>>9156092
>Now, it turns out that we can define what it means for a set to be finite (for example, if it cannot be put in one-to-one correspondence with one of its proper subsets)
Mmmm don't sets of size Aleph^1 do that?
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>>9156125
I meant Aleph 0, fuck.
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>>9155881
I think that OP is talking about all math concepts that do not have names like "Euler's circuit" and are given names that would seem to be self-explanatory but instead are misleading.
If we say that a number is whole then it is pretty easy to guess that it is without a decimal or fraction. If we instead say that a number is rational then we should know what a rational number is not because of its name but instead because of the examples and literature that probe into what rational numbers are.
I think the same issue plagues quantum physics. If quantum physics was instead called non-deterministic physics or non-newtonian mechanics there would probably be virtually no pseudo-scientific discussion about it.
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>>9156151
>we should know what a rational number is not because of its name
>ratio-nal numbers
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