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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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>>9147282
>Surely that is unsatisfactory
how ? even a brainlet can understand this, it is simply a set that contains more elements then any subset of it containing a natural number of elements .
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An infinite set is a set that you can't map a finite set into. It's not particularly ambiguous or ill-defined. Considering the practical applications of the results of Real and Complex Analysis. It does not particularly matter whether or not they "actually exist", i.e. if the universe is actually some plank-intervalled machine that is using mechanics which only "approximate" infinite continuity; infinite sets and Cauchy sequences have already proven their worth.
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>>9147490
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So what is a "circle"? Well, to begin with, you should say precisely what the word means.
Euclid decreed that a "circle" is a plane figure bounded by one line such that any line passing through the center point is equal.
Surely that is unsatisfactory, as Euclid himself no doubt suspected. It's like declaring that an "ultra unicorn" is a unicorn that is above all others, or a "straight OP" is an OP that is less gay than all other OPs. These are semantic constructs that have no mathematical meaning.
Surely no scientist would ever suppose that a """"""circle""""" exists. If you asked Neil DeGrasse Tyson if there existed any one-dimensional planar figure of points equally spaced from a center point, he would probably say: No. Even if there was a such an object, it's unreasonable to suppose you could draw it.
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>>9147515
kek
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>>9147490
>An infinite set is a set that you can't map a finite set into.
Define the function f:{1} -> ℕ by f(1)=1. There, I just mapped a finite set into an infinite set. Checkmate atheists.
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>>9147515
>>9147490
>>9147282
Wilderburger is embarrassing. Instead of advancing an alternative to current mathematics purely because of the computational benefits it may present he has to make this shitty horrible argument that current mathematics isn't logically consistent, while giving no logical proof of this. It seems really he uses "logically consistent" to mean "I don't believe it" which is obviously a pathetic thing for any trained professional mathematican to do
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>>9147282
an infinite set (A) is a set that has proper subsets with the same cardinality as A.
I think that's quite unambiguous. Also. may I remind you that not everything defined in math has to be "real". It's just a definition, and you can assign meaning to it if you want to, but at the end of the day it doesn't have to be more than a definition. Also, you're forgetting that the infinite set is an axiom, so it doesn't have to be proven real - you just need it to be consistent with the other axioms.
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>>9147282
What is a set, OP? You seem to be knowledgeable enough to say precisely what the term means.
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>>9148980
he meant isomorphic to or bijective to
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>>9148980
That's to it, not into it.
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>>9149009
>doesn't know what into means
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>>9149009
you are probably thinking of and "onto map". not the same thing my dude.
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