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
So what about an "infinite set"? Well, to begin with you should say precisely what the term means
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>a thread died for this
>neither I, nor my friends understand the concept, therefore the concept doesn't exist
>pooinloojuan
>enlightened
Have you guys read this essay by Zeilberger? Entitled “Real” Analysis is a Degenerate Case of Discrete Analysis
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Assume no infinite set exists
Integers are therefore finite
Integers are well ordered
Therefore you should be able to tell us what the maximum integer is, no?
how does the final question follow?
>Cantor declared that an "infinite set" is a set which is not finite. Surely that is unsatisfactory
Why? That's often how words that are grammatically the opposite of another word are defined. An irreducible polynomial is one that's not reducible, a connected set is one that's not disconnected, etc.
>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.
But I can show you an infinite set whose existence doesn't contradict any of the commonly accepted axioms of mathematics. Watch this: [math]\mathbb{N}[/math]
>Certainly in science there is no reason to suppose that "infinite sets" exist.
When are infinite sets used in science?
Q.E.D fuckers.
But in all seriousness, how is it that the concept of infinity is so hard to grasp for some people? Math deals with abstract constructs, it's illogical to try to bring it to the real world context to, somehow, prove that it doesn't make sense. Numbers are the best way to understand the concept of infinity, don't try to look at it in "real world glasses".
ebin