Artemus
Veteran Member
Do you believe that the only mathematical concepts that relate directly to "the real world" are arithmetic operations on the natural numbers?
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The meaning of infinity
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Do you believe that the only mathematical concepts that relate directly to "the real world" are arithmetic operations on the natural numbers?
untermensche
Contributor
I believe that some mathematical concepts very loosely relate to reality.
It takes a human mind and abstraction to make the relation.
So 1 can exist in that 1 apple can exist.
It is a very loose relationship.
And some concepts, like negative numbers and zero and infinity do not have real world correlates.
Things like geometric shapes do not exist for real. They are idealizations.
bilby
Fair dinkum thinkum
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If you can't prove what you believe, then nobody needs to give a crap.
People believe all kinds of crazy shit. Nobody else needs to care.
Proof, or GTFO.
The mathematics forum is not a suitable venue for religion, or for statements of faith.
Phil Scott
Member
Well said. And to clarify: formal definitions, then proof, or GTFO. Euclid's Elements opens at definitions, and its basic template for doing maths hasn't changed in the last two millenia. If untermensche wants to play a different game, he should join all the other cranks on a forum called untermaths.
untermensche
Contributor
I was asked what I believe.
Is there a proper way to think about how numbers relate to the world?
If so please tell us.
Does 1 exist in the real world apart from it's usage and definitions and symbols in mathematics?
Fill me in.
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I was asked about the relationship of mathematics to the real world.
If you think they are the same thing that is a strange religion.
Phil Scott
Member
Who cares? It's got nothing to do with the maths forum. What has got something to do with the maths forum is the basic fact that 0.999...=1, which is not settled by interrogating the real world, but by a bunch of abstract formal definitions.
By all means, take those abstract formal definitions to just be the rules of a game that a bunch of ivory tower mathematicians like to play, with no relevance to the real world. You can join in the game without taking it seriously. I only point out that if you're not following them, and you're not providing your own formal rules, you're not doing maths.
If you don't care about this stuff, GTFO.
untermensche
Contributor
I'll ask again.
Is 0.9 = to 1.000...
Is 0.99 = to 1.000...
Is 0.999 = to 1.000...
Is 0.9999 = to 1.000...
Is 0.99999 = to 1.000...
Is 0.999999 = to 1.000...
At what point does 0.999... become = to 1.0000
Which digit down the line?
Or is it just something you imagine that happens somewhere?
Phil Scott
Member
"0.999..." is a notation. It is a symbol. It is a sign. It has a formal designation. Nothing happens with that sign. You just follow the designation and throw up the easy equality 0.999...=1.
I'd love to talk you through this, but it means you giving up your calculator intuitions and exhibiting reading comprehension, and that's never going to happen.
untermensche
Contributor
It is a designation of an infinite operation.
It is not a designation of a completed infinity.
The completion occurs only in the mind.
It's impossible in notation.
It is a difference that is infinitely insignificant but a difference, unless one mentally completes the infinity.
In the real world differences that are infinitely insignificant can be discarded.
Phil Scott
Member
untermaths!
untermensche
Contributor
It is called not completing the infinity mentally then proclaiming, "wow the infinity completed!"
It is called not calling 0.9999.... a completed infinity. That is done purely arbitrarily.
It is a completed definition of an infinite operation.
To not know the difference is amazing.
Phil Scott
Member
You realise you're supposed to play Solitaire on your own, right?
Whenever you're done talking your own private language, let us know. Until then, GTFO.
untermensche
Contributor
The language is English.
It is not my own.
Your refusal to understand is noted.
You imagine infinities completing so they do.
In your mind.
Nowhere else.
DBT
Contributor
If the Universe is a part of a larger system, perhaps infinite, eternal space in which infinite numbers of 'universes' appear, evolve and die heat deaths, or retract and recycle, then that infinite and eternal space - being an actual Infinity - is complete and always was complete.
You may claim that such a thing is impossible, I'm sure you will, but there is nothing to exclude the possibility of Infinite space.
untermensche
Contributor
An infinity is defined as something that never completes.
It is not a real-world concept.
There is nothing natural about infinity.
Everything about it is arbitrarily defined.
But once defined you are stuck with it.
Although some do pretend an infinity can complete and don't even know they are pretending. They confuse pragmatism with natural consequence.
Phil Scott
Member
Which isn't sufficient. Maths is a technical subject and at this level needs more that an English language qualification and experience with a calculator. If you want to play this game, you have to learn the correct maths terms, grok their usage and imbibe formal definitions. I have provided numerous such definitions in this thread. Ask if you don't understand them and want to learn something. I enjoy teaching, but only people who can recognise they have stuff to learn. Otherwise, forget this discussion: it really isn't of any practical importance. Or if you want to keep pretending, at least crawl back to the philosophy forum where idiosyncratic and uneducated wibbling is better suited.
I have not said anything even vaguely resembling this so you are mind reading my maths posts based on zero knowledge of maths. That's some powerful arrogance. Do you subject the physics experts to the same treatment?
For the record, I do not take 0.999… to be an infinite object. I formalise it as a pair whose first component is the integer 0 and whose second component is a function which outputs 9 whatever the input.
I have a definition giving the conditions under which objects of this type can be treated as equivalent in certain circumstances, in turn parameterised on arbitrary error thresholds. When I then use my original objects to refer to the resulting equivalence classes, I see that the pair whose first component is 0 and whose second always outputs 9 belongs to the same class as the pair whose first component is 1 and whose second component always outputs 0. I write this:
0.999… = 1
By writing this, I am not thinking I have done any magical completing of infinities. I have just followed my finite collection of definitions.
If you object to the definitions, we can discuss that. But so far, virtually no one in this thread has bothered to engage those, instead contenting themselves with calculator reasoning and naive algebra. I consider that way below the dignity of a mathematics subforum.
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DBT
Contributor
Is that so? Who (besides you) defines infinity as ''something that never completes?''
untermensche
Contributor
untermensche
Contributor
You have no magic knowledge beyond the English language.
If they try to tell me shit is caviar they do.
You are claiming without any reason to believe you that 0.999... is equal to 1.000....
Great.
You have your little idiosyncrasies. They are your idiosyncrasies and nothing more.
You can do anything if you refuse to examine the object or if you look away from the object or if you subject the object to meaningless operations.
The object is [0.999....]
Nothing else.
That is (in English) a zero, a decimal point, and then an unending string of nines.
Unending.
0.9999.... never becomes 1.000...
Unless one has your peculiar idiosyncrasies.
Phil Scott
Member
Everything I've said in this thread can be found in the maths textbooks, so these ideas are hardly my "idiosyncrasies".
I guess you don't know what that word means. You don't know maths or basic English.
Ah well.
I guess you don't know what that word means. You don't know maths or basic English.
Ah well.