Should infinity be removed from mathematics?

Denis

Math Team
Oct 2011
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1,026
Ottawa Ontario, Canada
I can't believe that I am now creating "reply #81" to this thread...
And reply is: can someone please accidentally close this thread?
 
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topsquark

Math Team
May 2013
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The Astral plane
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99999994545757654687684

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99999994545757654687685

35438465131351868164687698465132138546849846916513 51849846914616516984984968465164984984984658168498 79765648684984161468496416468168468468468461513213 54687498798416513546846816135345846187191965146849 84984646816846846984684684649449879798784684687999 99999999999999999999999999999999999999999999999999
99999994545757654687686

35438465131351868164687698465132138546849846916513 51849846914616516984984968465164984984984658168498 79765648684984161468496416468168468468468461513213 54687498798416513546846816135345846187191965146849 84984646816846846984684684649449879798784684687999 99999999999999999999999999999999999999999999999999
99999994545757654687687

...that's the last time I do this!
That's the number of women who won't go out with me.

-Dan
 
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Aug 2012
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So why not say something like "as x increases indefinitely"? Using the word infinity carries with it the notion that something can be non-finite, which to my mind adds mysticism.

Everyone keeps saying that it does not matter what words we use or even if they have multiple definitions because it is the context that matters. But why choose words that carry weird connotations when we can choose words that bring clarity?
@Karma Can I ask you a question? When you see or hear about an infinity pool, do you write a letter to the city planning commission that they should rename it the "endless" pool or the "unbounded" pool?

When a car maker comes out with a product call the Infiniti, do you complain that they should not use a mystical word to describe the name of an automobile?

What exactly is your objection to using a particular word as technical jargon? After all in computer programming (your claimed field of expertise) we have something called a "loop." What would you say if I complained bitterly that the word "loop" refers to a piece of string with its two ends tied together; but a loop in programming may terminate? The horror! We've misused a common English word in a technical setting.

You'd think I'm being silly if I complained about the fact that the technical meaning of a loop is different than the common English meaning. And what if I dislike the use of the word "object" in the programming profession? After all that's a very vague and general word in English; but it's a highly specific and technical concept in computer programming. Same set of issues. You'd think me silly if I demanded that people stop talking about object-oriented programming.

What on earth are you going on about, if the extent of your concern is the use of a word? You have a bigger beef with the Nissan corporation, which produces the Infiniti, than you do with mathematics.
 
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Oct 2014
62
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UK
But I certainly don't accept your argument that they pop into existence when first summoned! That sounds silly.
I do not think they pop into existence.

I think you misunderstand what I mean by existence. A number can be written down, thought about, expressed on a computer and so on. It needs somewhere to appear, even if this is just somewhere in the human brain.

The same goes for any abstract idea. Abstractions are not physical objects that have an existence of their own in the real world. They are ideas we create and document.

I do not believe there is an infinite number of numbers existing in some invisible eternal realm somewhere. To me, this is a philosophical idea that is no use in practical terms because we have no way of accessing this realm, or do we (if so, how)?

I do not believe that this abstract collection of infinite numbers exists at all. Thus I do not believe that numbers just pop into this type of existence when first summoned.


OK, but v8archie's underlying point remains. If you take some big enough random number B, then with very high probability no person or computer has processed, looked at, thought of, etc. B, B+1, or B+2. So if you have a computer pick B and print B and B+2 (thus bringing them into existence), you have two consecutive integers which are both even or both odd, at least until someone computes B+1. Doesn't that strike you as strange?

Again, our understandings of 'existence' are very different indeed.

When a computer or human does a subtraction, they simply follow the rules explaining how to perform subtraction for the relevant number type.

There is no need for infinite sets.
There is no need to fetch numbers that already exist from an intangible infinite realm somewhere.
And it all works fine.

I could define my own formal system of objects and operations. I could define apples and pairs and work with these, not numbers. I could define what addition means and other operations. Or I could just create my own functions and operations such as ‘blend_textures’. Would I have discovered this from the infinite realm of mathematical truths or does it only contain numbers?
 
Oct 2014
62
2
UK
Induction is not a process. It is two statements of fact. The first provides a base for the second. It doesn't take any time for induction to work, it is simply true for all n greater than or equal to the base (n≥0 in this case)
Fair point :)

But I maintain it does not demonstrate that a completed infinite set can exist.

There are many prominent mathematicians who still refuse to believe that an infinite set can exist. You will find their names on the Wiki pages for finitism. It is not just me that finds this topic problematic.

I guess there is no real proof, you just believe in the concept or you don't.

Also, my previous post might clarify my views on numbers existing.
 
Oct 2014
62
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UK
I'll bite. What do you mean by existence?
This is off the top of my head. It is just my instinctive view, as I have not given it any serious thought.

If we think of a number then that thought has a physical manifestation in terms of chemicals, synapses or whatever in the brain. If we write a number down on paper then it has a physical existence in terms of the graphite or ink we use.

Without any physical manifestation a number cannot intrinsically exist, unless we believe in the supernatural.

If I thought about it longer I’m sure I could give a better description.
 
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Denis

Math Team
Oct 2011
14,592
1,026
Ottawa Ontario, Canada
I think you misunderstand what I mean by existence. A number can be written down, thought about, expressed on a computer and so on. It needs somewhere to appear, even if this is just somewhere in the human brain.
I'm the proud originator of post #89, previously not in existence...

If a tree in a forest falls, is there any sound if nobody is within hearing distance?

If there was an undiscovered little island somewhere, do the snakes living on it exist?
 
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Jul 2010
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St. Augustine, FL., U.S.A.'s oldest city
...If a tree in a forest falls, is there any sound if nobody is within hearing distance?...
Only if a bear is doing his business nearby...
 
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