the set of numbers between 1 and 2, is a smaller set of infinite numbers between 1 and 3 — Vaskane
Even still infinity as a noun is relevant to mathematics in numerous ways like [...] — Vaskane
It makes no difference. — Philosopher19
You keep saying I ignore your points, but rightly or wrongly, I also think you have not read or considered what I've written with sufficient attention to detail. — Philosopher19
I do think that I am being sincere and honest in this discussion (as well as not closed-minded). — Philosopher19
If you understand that our brains are churning out stand alone theories that work fine in a certain context but don't all work together in every context [...] — Mark Nyquist
OK.I don't mean to use Existence loosely/abstractly. By "Existence" I mean that which encompasses all things physical or otherwise (if otherwise is possible). — Philosopher19
I guess this "something" is "space", right? Like a balloon ...If the universe is expanding, it is expanding in something. — Philosopher19
OK.So to me, Infinity/Existence is the reason that something can expand forever or go on forever. As for the thing that expands (like the universe), it is a part of the Infinite. It is not itself infinite. — Philosopher19
On the basis of mathematics it's quite easy to detail larger and smaller sets of infinite numbers, like the set of numbers between 1 and 2, is a smaller set of infinite numbers between 1 and 3. [emphasis added] — Vaskane
By Being. Existence just Is. It just is the case that triangles are triangular or that Existence is Infinite or that 1 plus 1 = 2 — Philosopher19
But you did not say how.The angles in a true triangle add up to 180 degrees because that is the nature of Existence
Cardinality and Size aren't the same. (..) The interval between 1 and 3 is 2 and thus larger than the interval between 1 and 2 which is only 1.
it's quite easy to detail larger and smaller sets of infinite numbers, like the set of numbers between 1 and 2, is a smaller set of infinite numbers between 1 and 3. — Vaskane
Unfortunately for you the interval between 1 and 3 is 2 and thus larger than the interval between 1 and 2 which is only 1, and thus quite simple to show that having two intervals of infinity is twice the size of one interval of infinity. — Vaskane
Consider it a contextual error of considering area as size? — Vaskane
Doesn't infinity mean endless? i.e. unreachable eternal continuation in concept? — Corvus
If it was reachable, then it wouldn't be infinity. Any set or size would be unknowable, if it were infinity. Therefore talking about different size, set or number of infinity, is it not a nonsense? — Corvus
That's a matter of perspective really, I was a Navy Cryptologist, that you only view numbers as a row and now both rows and columns, again revolves back to your objective perspective. — Vaskane
I think it's nonsense to say Infinity comes in various sizes. — Philosopher19
I guess this "something" is "space", right? Like a balloon ...
But this seems impossible since space is part of the universe itself; it cannot be larger than it. E.g. like the space around a balloon that is inflated ... — Alkis Piskas
Do you agree that lines have length? — Vaskane
He still persists in mischaracterizing mathematics as claiming that there is an "Infinity" [capitalized, no less] that has different sizes — TonesInDeepFreeze
That is egregious intolerance — TonesInDeepFreeze
It makes a real difference. By saying 'infinity' as a noun and then that there are different sizes of infinity is to picture an object that has different sizes. There is no such object in mathematics. — TonesInDeepFreeze
Good faith in posting a critique of mathematics would entail at least knowing something about it. — TonesInDeepFreeze
But from what I've seen of mathematicians, they either have no part for infinity, or they're using infinity wrong. I believe they're doing the latter which leads to the former (which I think is why I have heard it said before that "maths is incomplete") — Philosopher19
But from what I've seen of mathematicians, they either have no part for infinity, or they're using infinity wrongly. I believe they're doing the latter which leads to the former (which I think is why I have heard it said before that "maths is incomplete") — Philosopher19
To my understanding, mainstream maths claims:
There are infinites of various sizes (or at least infinite sets of various sizes, but that amounts to the same thing)
The set of all sets is contradictory — Philosopher19
if someone came to me and said they have demonstrated how infinity comes in various sizes, I would say to them that that's nonsense to me. — Philosopher19
Cantor’s Theorem and the Unending Hierarchy of Infinities: still hasn't been disproven;
"For instance, by iteratively taking the power set of an infinite set and applying Cantor's theorem,we obtain an endless hierarchy of infinite cardinals, each strictly larger than the one before it. Consequently, the theorem implies that there is no largest cardinal number (colloquially, "there's no largest infinity")." — Vaskane
Cantor treats a number sequence that goes on forever as being infinite. But something going on forever does not make it infinite (if my counting to infinity goes on forever, that neither makes my counting infinite, nor does it mean I will eventually reach infinity). It also makes no sense to say something like "assume that your counting to infinity is completed such that you have counted the set of all natural numbers and have successfully proven that there are an infinite number of natural numbers" and then label this as {1,2,3,4,...} — Philosopher19
And that's why I make a great analyst because I have an ability to understand concepts without even knowing of them — Vaskane
But from what I've seen of mathematicians, they either have no part for infinity, or they're using infinity wrongly. I believe they're doing the latter which leads to the former (which I think is why I have heard it said before that "maths is incomplete") — Philosopher19
Yo, like I said, I came here making a comic relief joke, to which it tumbled into the argument on the size of infinities, and lo and behold I have an actual theorem that shows sets of cardinals being larger than the last, that backs me up and it's a theorem that has had impact upon reality my friend: Theory of Computation: Cantor's diagonal argument, used to prove the existence of different sizes of infinity, inspired Alan Turing's work on the undecidability of the halting problem, a foundational result in the theory of computation and computer science. — Vaskane
Still Cantor proves Cardinals do indeed have varying sizes. — Vaskane
Maybe a winter pastime for some of us. — Mark Nyquist
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