## Proof that infinity does not come in different sizes

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• 729
I'm really sceptical of the idea that there is any one true math to decide these issues of infinity.

To me the best we can do is categorize models of infinity as conceptual mathematical objects.

As such the parameters are arbitrary and their usefulness is in a defined mathematical environment.

Under this categorization scheme, it can be possible that one model can be inconsistent with another and not be false.

Here is my example,
A smaller infinity can reach any finite number that a larger infinity can by freezing the larger infinity and letting the smaller one catch up.
I'm sure there are all kinds of problems with this in the standardized mathematics but in the sense of a conseptual mathematical object it is legitimate. I think I first said it as a bit of a joke but the idea is we can drive the math by abstractions.
• 2.3k
I'm really sceptical of the idea that there is any one true math to decide these issues of infinity.

We'd have to look at the arguments of people who have said that there is. Who do you have in mind? Naturally, we would look at realists such as Godel. And there are also cranks who at least present as if their own vague, undeveloped, impressionistic and incoherently suggested concept is the true concept, as meanwhile they do explicitly represent that classical mathematics is false.
• 2.3k
it can be possible that one model can be inconsistent with another and not be false.

I'd rather say 'theory' than 'model'.

But then we must ask what we mean by a theory being true or false. In a rigorous sense, a theory is true or false in a model for the language for the theory. A theory may be true in some models and false in others. And of course, if a theory T is inconsistent with a theory S, then there may be models in which T is true but other models in which S is true.
• 2.3k
A smaller infinity can reach any finite number that a larger infinity can by freezing the larger infinity and letting the smaller one catch up.

Define 'reach', 'freezing' and 'letting catch up'. Better yet, tell me your primitives and your sequence of definitions from the primitives.
• 729

What I've written is about as far as I've gotten on a 'theory'.

I was thinking there might be an application for this in central banking or distributing resources to competing unlimited wants. Maybe the math is out there in some form already. Wouldn't doubt it.

What about two infinity generating machines that spit out consecutive integers at variable speeds endlessly.
Set a dial and one or the other can go faster or slower or stop. If you have a system like that matched to physical systems that have finite limits it might be an interesting model

I'm in over my head but don't infinities have some rubber band like properties that can be set at will.

My interest is mostly going from brain state to doing the math as a basis for a philosophy of mathematics..... Real simple,. Brain; (math processes)

Don't expect everyone to do it perfectly and in learning math or new skills it's always a process of brain programing.

Fight the cranks all you like. Makes things interesting. It's just philosophy here not pure math.
• 2.3k
It's just philosophy here not pure math.

I have addressed that so many times in so many threads. Maybe earlier in this thread too.
• 8.7k

When in over one's head, it is recommended to keep one's mouth shut, and head for the shallows. People have drowned in these waters.
• 729

I've had college algebra, trig and calculus.
I can also design trusses and figure pressure loss in pipelines. Doesn't that sound exciting.
• 849
I can also design trusses and figure pressure loss in pipelines. Doesn't that sound exciting.

No, I hate trusses. But hey, more power to civil engineers, though I would rather let the computer handle all those forces in different joints. Don't ask me about hyperstatic structures — I don't know.
• 8.7k
I've had college algebra, trig and calculus.
I can also design trusses and figure pressure loss in pipelines. Doesn't that sound exciting.

Well then, when in over your head, retreat to dry land and build a bridge.
• 729

I don't really design trusses but in addition to course work I made my own collection of scale model trusses of various designs. I still have them in a folder somewhere. Glue and cardboard.
• 3.5k
I believe the solution to Russell's paradox is in here:

Honestly, I am having trouble dissecting the arguments used here.
Thoughts, jgill ?

Russell's Paradox and infinity arguments hold no interest for me. After going round and round with the author on First Causes, I suspect I would learn little from this paper.
• 12.3k
I can also design trusses and figure pressure loss in pipelines. Doesn't that sound exciting.

I'm interested to know exactly how pressure is lost in pipelines, if there is no leaks. I've heard that in the USA a huge amount of natural gas just goes missing. Where does it go?
• 22.9k
I've heard that in the USA a huge amount of natural gas just goes missing. Where does it go?

(Ok, but someone had to say it...)
• 729

Friction loss but it's way off topic.
• 814

Infinity is more of a process of continuing than a quantity?
• 273

I don't think the process of continuing forever amounts to anything infinite. I see infinity as the reason for the process of continuing forever as being possible/meaningful.

To me, Infinity and Existence denote the same.

I see Existence as the set of all trees, humans, numbers, existents/cardinalities. I see the set of all existents/cardinalities as Infinite. I'm not sure if I should describe Infinity as a quantity here or not. But I think something like 'the cardinality of absolutely all existents (so that's all numbers, letters, trees, semantics, hypothetical possibilities and so on), amounts to Infinity'. I don't see Existence as incomplete because such a view runs into contradictions, hence the need for Existence to equal Infinite (and possibly the need for Infinity to equal a quantity representative of the cardinality of absolutely all existents).
• 22.9k
To me, Infinity and Existence denote the same.

:roll:
• 999

According to the philosophy of intuitionism, a sequence that is said to be "without an end", is only taken to mean a sequence that is without a defined end. This is similar to computer programming, where an infinite loop that is declared in a computer program is only interpreted to imply that the program is to be stopped by the external user rather than internally by the program logic.

So in intuitionism (and computer programming), the difference between a finite sequence and an infinite sequence is taken to be epistemic rather than ontological. From the point of view of the producer of the sequence who gets to control it's eventual termination, the sequence could be said to be "finite", whereas from the consumer's point of view who has no knowledge and control of the sequence's termination, the same sequence could be said to be "infinite", or better, "potentially infinite". Or even better, the word "infinity" can be deprecated and replaced by finer-grained terminology that precisely conveys the information that one has at one's disposal in a given situation, without committing to the idea that the information one has is complete.

Amateur (and even some professional) philosophers demonstrate a profound gullibility, in their face-value interpretation of mathematical symbolism. To believe that infinity means "never ending" in an absolute sense just because an upper bound is omitted from a definition, is like believing that a blank cheque cannot bounce.
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