General Question

Blondesjon's avatar

Do you believe in the concept of infinity?

Asked by Blondesjon (32156 points ) February 2nd, 2009 from iPhone

My 16 year old (the math whiz) just told me he wanted to prove that infinity does not exist. His argument was based on the inherent paradox in a universe of ‘infinite possibilities.’

I told him I would become a believer when he told me what the ‘last’ number was.

It got me to wondering though…

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44 Answers

Perchik's avatar

Until you can prove that there exists a number, in which you cannot add 1 to, infinity exists.

MrItty's avatar

Your 16 year old’s logic is flawed. Just because infinity is a valid mathematical concept, it does not logically follow that there are “infinite possibilities”.

That sounds far more like a theory of multiple universes than anything else.

Vinifera7's avatar

Uh oh.. MrItty’s here. I wonder if he’ll bark at me again.

The concept of infinity exists as long as we can conceptualize it. That doesn’t mean that there are infinite possibilities or infinite anythings though.

So if you mean “believe in the concept of infinity” as in “believe that the concept of infinity exists”, then yes I do.

AlfredaPrufrock's avatar

I think the infinity that exists between 0 and 1 is bigger than the infinity of whole numbers.

“Infinite possibilities” is not correct because “possibilities” are subject to constraints. I think, as they say, your son is mixing pigs in with the chickens.

Vinifera7's avatar

It’s not bigger or smaller. It’s infinite.

laureth's avatar

There are also different sizes of infinity. That almost broke my brain.

artificialard's avatar

My eyes sees words in that article but my brain is all “bleeerrrrrg”.

cdwccrn's avatar

Infinity exists. Good luck finding it.

fireside's avatar

According to the law of conservation of energy; energy can neither be created nor destroyed but only changes from one form to another.

If that is accepted as true, then so must be infinity.

jackley's avatar

The nature of Infinity is something I ponder quite a bit.

How can a finite being possibly comprehend an infinite existence, or an infinite amount of space or time? We have no concept of it because we cannot experience it; we live in a finite universe; our lives our measured in finite terms.

Also: some people imagine “infinity” is a place that you arrive at once you count long enough, or something similar. Quite ridiculous.

A theology teacher once described “infinite” to my class as this:

Imagine a seagull on a beach. Now imagine that seagull picked up a single grain of sand and flew to the Sun and back. Imagine that it repeated that process for every single grain of sand on Earth.

Still, even that would end at some point.

jackley's avatar

@fireside Can you elaborate on your reasoning?

fireside's avatar

If energy cannot be destroyed and can only change form, then energy must continue on ad infinitum, in some form or another.

AstroChuck's avatar

My neighbor used to work at an Infiniti dealership, so I know the concept exists.

TaoSan's avatar

@AstroChuck

How come that scrolling down the posts I was kinda waiting for you to come up with that? :)

Christian95's avatar

I don’t think infinity exist.For me ’‘infinity’’ is just that part of the universe that we don’t understand NOW.If you look back in history you’ll see the most important clue:at the begging the ’‘infinity’’ was much more larger than today because at that time the people were very limited(the brain I mean) and now infinity is smaller.So from here you should understand that does not exist and this will be proved in the future when we’ll be more intelligent and we’ll be able to understand.

mea05key's avatar

i dont think infinity ever exist for me as well. I would say its more like an assumption.

Looking at nature, for example a tree. A tree has a branch which then multiply to smaller branches, twigs and so on. The smallest particle would be the nucleus of the tree cell. That’s where we stop. That’s the basic thing that makes up all organism and for inorganic material, the atom or more precisely the proton, neutron and electron that describe the matter. The amount of energy that is contained in the universe i believe is finite as well.

fireside's avatar

I think about the light from stars that we can see. Some of those stars no longer exist, yet we still see the energy that left them thousands and thousands of years ago and that energy doesn’t just stop when it passes us.

MrItty's avatar

Vinifera, I will continue to “bark” at you so long as you keep making false assertions about topics with which you are not familiar. This one is no exception.

As AlfredaPrufrock and laureth have pointed out to you, there are indeed different sizes of infinity. The infinite number of values between 0 and 1 is greater than the infinite number of whole numbers.

This sort of thing can be mathematically proven. Please stop making assertions without doing a little bit of research to find out whether or not you know what you’re talking about.

And this response, if you were wondering, is a direct result of your uncalled-for attack “whisper” in your first post in this thread.

Perchik's avatar

MrItty. Chill out. You’re making the rest of us mathematicians look bad. Stop being arrogant. If people are wrong ,correct them nicely.

Jeez.

MrItty's avatar

I gave up being nice to him in the last thread in which he took it upon himself to not only be wrong – which is perfectly valid – but also to insult the person asking the question. That is not valid, and not acceptable.

Perchik's avatar

Insulting the original poster is wrong, but insulting other members is perfectly acceptable? Ah I see now.

MrItty's avatar

Explain to me what I said to him that was an insult? Did I call him names? Did I say his mama’s so fat? Did I, like he, label his words “nonsense”? No. I stated nothing but facts:
* He makes false assertions, in both this thread and the previous;
* he started his post in this thread with an uncalled-for attack on me;
* There are different sizes of infinity;
* He does no research before posting his incorrect information as fact.
* When it comes to infinity, he does not know what he is talking about.

Are any of those insults? I’m truly sorry if you think so. I respectfully disagree.

If he would just man-up and issue an apology to the OP of the original thread, like he should have in the first place, I’d be content to never respond to him again. Instead, he chooses to not only not own up to his wrongdoing, but then to continue his attacks on me in subsequent threads. So yes, I will continue to call him out on it.

TaoSan's avatar

My aren’t we touchy???

And all without even mentioning Dedekind or Cantor.

@Mritty

With all due respect, I don’t see anything in Vinifera’s post that would be a “false assertion”. Smacks a lot of grudge. I think the moderators are fully capable and speedy in noting and responding to posts gone awry. No extra policing necessary.

Relax…

And by the way, ya’ll fail to make the distinct determination between mathematical infinity and philosophical and theological infinity, the latter two being an entirely different bag of beans than the first one.

MrItty's avatar

Tao, I the false assertion is Vin’s second post, telling Alfreda that she was wrong about the two sizes of infinity.

As for “grudge”, yeah more or less. You’ll note the very first sentence in Vin’s first post in this thread is an attack on me. I know it sounds like a five year old’s defense, but frankly, “he started it.”

steelmarket's avatar

Try watching a Growing Pains marathon, you will understand the concept.

TaoSan's avatar

@MrItty

a little snippy maybe, but not really an attack. Things can come across all sorts of ways if you don’t see a face on the other side.

Just thought I’ll add some perspective, it didn’t look that “attack’ish” from a 3rd party standpoint

as for “bigger” or “smaller”, again, it is not that easy really. Both are right, there are different manners of expression. I can only again reference to Dedekind and Cantor, as it would by far exceed the scope of a post here to even only scratch on their modeling.
Philosophy and higher math do have a blurry line sometimes.

Bri_L's avatar

In my opinion infinity exists because we created and defined it. we set up a numerical system by which you can always ad one. So, just keep doing that. Or, tip and “8” on its side and be done with it.

artificialard's avatar

@fireside What does a poop have to do with the question?

AstroChuck's avatar

@artificialard- I think what fireside is trying to say is that Mr. Hankey is infinitely endearing to all.

finkelitis's avatar

@Blondesjon—what was your 16-year-old’s argument?

Also, what was he trying to prove, exactly? That infinity can’t exist satisfactorily as a concept? Or that you can’t find it out in the universe? Or that infinite universes can’t exist?

fireside's avatar

@artificialard and AC – Haven’t you ever had one that felt like it wasn’t going to end?

and why’s the character for infinity so small?

Blondesjon's avatar

@finkelitis…He said that it would prove so much established theory wrong that we would be able to start our search for the reason “why” from scratch.

He also hates paradox and said infinity reeks of it.

finkelitis's avatar

Infinity does reek of paradox. Aristotle tried the same tactic; some people argue that it put off the development of calculus by about 1500 years.

finkelitis's avatar

There are also a number of modern logicians who deny the axiom of choice (denying it prevents most meaningful manipulation of infinity) and see what they can build. They’re in the minority, but they’re out there.

finkelitis's avatar

Personally, I think that you get into the meat of things when you start confronting paradoxes (like your son is doing). That said, it’s unlikely that he’ll be able to prove it doesn’t exist. But infinity means different things in different places—sometimes it’s a surprisingly “finite” feeling object. Sometimes it’s bafflingly hard to contend with. Generally, it makes mathematics much better, stronger, more complete. Can you actually prove it exists? Depends what you mean by exists, and what axiomatic system you’re using to try and prove things. But there’s certainly no largest number, as you say.

finkelitis's avatar

The BBC just did a nice documentary about some of this called “Dangerous Knowledge.” I just linked to it on my blog. You can find it other places too, I’m sure.

I’m still curious what your son’s paradox regarding the universe of “infinite possibilities” is. He might enjoy looking at Zeno’s paradoxes too.

Perchik's avatar

Please don’t multi post just to post multiple times. You can edit a post if you forgot something.

Blondesjon's avatar

@Perchick…Is that because each post pops up as a new alert?

trying out my deductive reasoning

finkelitis's avatar

I was doing it because I wanted to respond before Blondesjon left. What’s the problem with multiposting? It just seems like a better stylistic way to break up thoughts. Is there any other benefit I could be after?

fireside's avatar

maybe you just really like seeing your avatar : )

Waffle's avatar

Infinity is an abstract representation of unlimited possibilities.

In math, it’s not something you can “believe in,” it’s just an abstract value.
In metaphysics, it’s a concept that can never be proven or disproved.

Blondesjon's avatar

jonsblond just cracked me up with rosemary’s fluther and when harry met fluther

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