Infinity cannot be divided, if it can then it becomes multiple finite objects.
It really depends on what you mean by infinity and division here. The ordinals admit some weaker forms of the division algorithm within ordinal arithmetic (in particular note the part about left division in the link). In fact, even the cardinals have a form of trivial division.
Additionally, infinite sets can often be divided into set theoretic unions of infinite sets fairly easily. For example, the integers (an infinite set) is the union of the set of all integers less than 0 with the set of all integers greater than or equal to 0 (both of these sets are of course infinite). Even in the reals you can divide an arbitrary interval (which is an infinite set in the cardinality sense) into two infinite sets. For example [0,1]=[0,1/2]U[1/2,1].
If infinity has a size, then it is a finite object.
Again, this is not really true with cardinals as cardinals are in some sense a way to assign sizes to sets.
If you mean in terms of senses of distances between points, in the previous link involving the extended reals, there is a section pointing out that the extended reals are metrizable, informally this means we can define a function (called a metric) that measures distances between points in the extended reals that works roughly as we'd expect (such a function is necessarily well defined if either one or both points are positive or negative infinity).
"The cardinality of the integers is equal to the cardinality of the real numbers, which is called the continuum hypothesis."
The cardinality of the integers is not equal to the cardinality of the reals. The integers are countable (have the same cardinality as the natural numbers). A very famous proof in set theory called Cantor's diagonal argument shows the reals are uncountable (i.e. not countable).
The continuum hypothesis is also not about comparing the cardinality of the reals and the integers or naturals (since we already know the above). The continuum hypothesis is about comparing the cardinality of the reals with aleph_1.
Within the usual set theory of math (ZFC set theory), we can prove that we can assign every set a "cardinal number" that we call its cardinality. For finite sets we just assign natural numbers. For infinite sets we assign new numbers called alephs. We assign the natural numbers a cardinal that we call aleph_0.
These cardinal numbers come with an ordering relationship where one set has a cardinality larger than another set if and only if its associated cardinal number is larger than the other sets cardinal number. So, alepha_0 is larger than any finite cardinal, for example. There is a theorem called Cantor's theorem that tells us we can continually produce larger and larger infinite cardinals in fact.
So, we know the reals have some cardinality, thus some associated cardinal number. We typically call this number the cardinality of the continuum. The typical symbol for this cardinality is a stylized (fraktur) c. Since aleph_0 is countable, every aleph after aleph_0 is uncountable. By definition aleph_1 is the smallest uncountable cardinal number. The continuum hypothesis just asks if aleph_1 and c are equal.
As an aside, it is provable that c has the same cardinality as the powerset of the naturals. We let the cardinality of the powerset of a set with cardinality x be written as 2x. Then we can write the continuum hypothesis in terms of 2{aleph_0} and aleph_1. The generalized continuum hypothesis just swaps out 0 and 1 for an arbitrary ordinal number alpha and its successor in this new notation.
This issue is not a black and white speak english vs not kind of thing. There's no shortage of immigrants that speak english perfectly well sans a minor accent but are discriminated against and treated poorly anyway for not being native speakers.
Edit for those who downvoted: I am a native english speaker. I have been discriminated against based on my regional accent. Only a fucking fool would think the same things don't happen to nonnative speakers.
Part of the goal here isn't even mastery of the language itself. Exposure to new cultures is important. Being able to empathize with how hard learning a language is is also important.
If you have a fixed collection of processes to run on a single processor and unlimited time to schedule them in, you can always brute force all permutations of the processes and then pick whichever permutation maximizes and/or minimizes whatever property you like. The problem with this approach is that it has awful time complexity.
Edit: There's probably other subtle issues that can arise, like I/O interrupts and other weird events fwiw.
Have you studied philosophy of religion? Sounds a lot like you haven't. Maybe reading up on it will help you? You can fix your reading comprehension and also learn not to say the dumbest shit possible on topics of religion. It's really a win-win for you.
Sorry for getting your panties in a twist over paraphrasing your totally irrelevant point. Please understand, I don't give a shit about what you think you can prove or disprove.
Any supernatural phenomenon, upon rigorous delineation, becomes provably false
Great point, one of the MAJOR challenges with arguments about whether a god does or does not exist is that the whole notion of a god is incredibly vague and not "rigorously delineated" in a general sense. Literally any introductory course in philosophy of religion would point this out.
The lack of reading comprehension here is definitely on your end.
Me (sans-snarkyness) in the original comment you replied to: "Hey, the field of philosophy where this stuff is studied is called philosophy of religion. Proofs for and against the existence of a god have been critiqued to shit there. You should read about it."
You: "Oh yeah! Well I can disprove any god you like."
Congrats? Do you want a gold star or something?
Go study philosophy of religion. These kinds of proofs and disproofs are part of that field along with their critiques. That's the point I'm making in the comment you originally replied to. Nothing about my point is subjective.
I'm "oh-so-focused" on that because you're "oh-so-focused" on telling me about "empirical investigations" that disprove the existence of gods, which have literally nothing at all to do with my point.
I never said there was prove god doesn't exist. And like I said, there doesn't need to be as long as there is no documented sign whatsoever that points towards god actually existing.
You also said: "A nonexistent almighty being". Did you mean no gods exist, or did you mean all the gods people claim to exist so far have been debunked?
More importantly, for the claim "no god exists" specifically, I disagree that no proof is required in general. There needs to be an actual proof as much as there needs to be a proof of the negation, that "a god exists", for either to be worth accepting. If neither can be proved, why commit to believing the truth of either?
Additionally, disproving particular examples doesn't prove the general rule. Having no documented sign pointing to the existence of a god does not confirm the absence of a god anymore than having no documented signs of a gas leak in your home confirms the absence of a gas leak in your home. Perhaps the detector you are using is broken, perhaps the type of gas leaking in your home is not detectable by your detector.
It would also be incredibly hard to design any kind of empirical test to confirm or disconfirm the existence of gods in general (not just the christian flavored ones).
It seems like you should understand my point/position before you reply to me if you want this conversation to be productive? Why is understanding those things irrelevant to you?
Why is it silly that the claim originally presented should have to present evidence first? The counter-claim only has zero burden of proof so long as the original claim has failed to give any proof of their own.
That's not what I'm claiming. I'm saying the claim AND counter-claim should provide evidence/proof before either one is accepted. Blindly believing not B because you can't prove B is just as bad in my opinion as believing B itself with no proof.
You wouldn't have to present an argument yet, at that stage. I'd think you're really dumb for needing something like that proven to you, but the initial burden of proof would still be on me. However, when I quickly and easily provide proof that 2 + 2 does equal 4, THEN the burden of proof falls to you to prove your counter-claim.
A lack of evidence or proof for some claim B is not sufficient proof for not B. It doesn't really matter what claim we assign to B here.
For example, you might not have evidence/proof that it will rain today (i.e. B is the statement "it will rain today"), that doesn't give you sufficient evidence/proof to now claim that it will not rain today. You just don't know either way.
It really depends on what you mean by infinity and division here. The ordinals admit some weaker forms of the division algorithm within ordinal arithmetic (in particular note the part about left division in the link). In fact, even the cardinals have a form of trivial division.
Additionally, infinite sets can often be divided into set theoretic unions of infinite sets fairly easily. For example, the integers (an infinite set) is the union of the set of all integers less than 0 with the set of all integers greater than or equal to 0 (both of these sets are of course infinite). Even in the reals you can divide an arbitrary interval (which is an infinite set in the cardinality sense) into two infinite sets. For example [0,1]=[0,1/2]U[1/2,1].
In the cardinality sense this is objectively untrue by Cantor's theorem or by considering Cantor's diagonal argument.
Edit: Realized the other commenter pointed out the diagonal argument to you very nicely also. Sorry for retreading the same stuff here.
Within other areas of math we occasionally deal positive and negative infinities that are distinct in certain extensions of the real numbers also.
Again, this is not really true with cardinals as cardinals are in some sense a way to assign sizes to sets.
If you mean in terms of senses of distances between points, in the previous link involving the extended reals, there is a section pointing out that the extended reals are metrizable, informally this means we can define a function (called a metric) that measures distances between points in the extended reals that works roughly as we'd expect (such a function is necessarily well defined if either one or both points are positive or negative infinity).