Math Philosophy-- Why does 1/∞ not equal 0, and for that matter, what is ∞?

Originally posted by circlemaker
reply to post by OutKast Searcher

 

1/finite meaning any finite number? Make more sense please.

I would love to...but I can't...because it makes no sense.

Which is exactly how I feel when you and others claim 1/infinity = 0.

In your mind, you have taken the concept of "infinite" as meaning some very large number. But it is just a concept...just as "finite" is a concept.

So you saying 1/"infinite" = 0 makes just about as much sense as me saying 1/"finite" = "something".

reply to post by PhysicsAdept
I think you may be overthinking the problem.

Lets look at it from an english standpoint.

The limit of 1/infinity is 0.

1/infinity is limited by 0. This means that 1/infinity, while it approaches 0 is never equal to 0. 0 is the limit.

Infinity as a concept is meant to mean that no matter how high or low you count there is always at least one number that is greater or less than what you are counting.

-saige-

Infinity, zero, God, heaven... all tied together, bound by our lack of understanding. Through faith we can achieve an understanding, though human words cannot express.

It also shows that you cannot put God into a box (bound by a finite number).

reply to post by circlemaker


Thanks for sharing that, I looked at it. Quite beautiful.

reply to post by OutKast Searcher


Once again you quip back with a condescending remark instead of answering a simple question. You really are a troll.

Originally posted by circlemaker
reply to post by OutKast Searcher

 

Once again you quip back with a condescending remark instead of answering a simple question. You really are a troll.

All I'm doing is looking for the answer to 1/finite.

You already claim to have the answer to 1/infinite...so this should really be no problem.

reply to post by ProgressiveSlayer


I believe I actually mentioned this sigma notation, I will provide a link if necessary. The fact that you believe .9r=1 (as well as I do) does however, IMO contradict what you are saying of infinity. What is the theoretical difference of 1 and .9r? .0r1 right? Is that not saying that 1/∞, which is equal to .0r1 is equal to 0??

And to say we cannot reach infinity may be true, however the point is that we are imagining we are there, in which case 1/∞ must be zero... We cannot reach 0 Kelvin, yet I fail to believe that we cannot conceptualize what happens when we do...

reply to post by charlyv

Infinity is a rational number.

It is not a number at all. People think that I use it as one, which is false, but It is not a number. It is a concept, yet within this concept is the ability to treat it as something similar to a number--with slightly different properties.

reply to post by Phenomium

Math is the mental cellphone....it serves nothing more than to distract. Outside of adding,subtraction,multiplication and dividing ...the rest is nothing but a mental workout with no payoff other than to say "I know this and you don't" Which is fair, but many other people know things that mathematician's don't. I really don't see why it matters.

Math is allowing you to be on the computer right now, so maybe you should be a little more grateful? If you care nothing of math, then why even enter this thread?

reply to post by Socrato


Well infinity is a concept, of course. Yet so is the whole numbering system and irrational numbers and so is the English language, freedom, and love, yet people still use those in daily life right?

reply to post by OzMan63


I am familiar with Cantor, as well as Euler who were both master explorers of the concept of infinity.

However two things to be kept in mind, their proofs (though not disprovable) do not proof much of anything except that infinities aren't larger than each other if they can be paired.

Ex: you can pair all whole numbers with odd numbers, and all fractions with even numbers and of course there are variations of each.... but, what about irrational numbers? There is no way to pair them, and thus you would appear to have a far greater amount of irrational numbers than rational, making one infinity greater than the other?

Ok well I can tell you are not convinced, but what convinces me better actually comes through with rates, in which you can see that here

Originally posted by robhines
The way I see it, anything divided by infinity ceases to be a number that can be defined because it's not fixed. So fixed maths numbers won't work here because you can't set a number, you'd just have to show it as infinity. Any number divided by infinity equals infinity because the division is never ending, it's turned into a perception of infinity or a non-stop stream of energy, or whatever else you want to call it.

Like if you say "what's the last number if you count to the end?" You can't count to the end because it branches off into the infinite.

edit on 19-3-2012 by robhines because: added

Not a horrible way to think of it, for sure, I actually mentioned this in my previous thread here in a way, but also... well read my others posts on this thread. No need to repeat anything.

What I understood of infinity, is that infinity stretches on forever and that any number is so small compared to an infinite number that multiplying or dividing into it makes no difference. The answer would still be infinite, but I am talking about dividing or multiplying by a positive number. Doing so by zero I haven't contemplated til now. If zero means none, nothing, nil, then you have none of whatever. zero apples times 3 is still zero apples, I still don't have any. But can infinity be divided or multiplied by zero, what does that mean? An infinite number of apples divided by zero, the zero becomes irrelevant relative to infinity's size, so the answer is still infinite? This is intriguing, what do other members think?

reply to post by PhysicsAdept


In my opinion , you can't really speak of infinity without getting Philosophical. infinity is common sense. As long as there are unknowns , there is the problem of infinity. What we try to do is restrain infinity and apply it to the world around us through the innumerable probability of ........... anything.

In my personal opinion , i see infinity has an expression of God. , a professor opened this theory when he spoke of it is as impossible for infinity to exist without an infinity.

Originally posted by CaptGizmo
Too deep for me, although there is one question regarding numbers that has always puzzled me.
Why don't we call the number 11(eleven) onety-one?

Eleven

Eleven in Old English is endleofan, and related forms in the various Germanic languages point back to an original Germanic *ainlif, "eleven." *Ainlif is composed of *ain-, "one," the same as our one, and the suffix *-lif from the Germanic root *lib-, "to adhere, remain, remain left over." Thus, eleven is literally "one-left" (over, that is, past ten), and twelve is "two-left" (over past ten).

Really maybe it should be pronounced One-one base 10 haha, I saw that on askville.com

Originally posted by PhysicsAdept
reply to post by circlemaker

 

Thanks for sharing that, I looked at it. Quite beautiful.

I'm glad someone appreciates it. You might also find the "root circle" section interesting. Not only do I show how to make a circle algorithmically without any knowledge of pi, I show where conventional math breaks down using an interactive example.

reply to post by assspeaker


Well if you want to go philosophic, wouldn't infinity include everything? It would include all numbers, both rational and irrational, as well as imaginary numbers, and... dare I say... 0?

reply to post by johnquindell


No I think it is a great question--one I wish I knew the answer to

People on here argue very well that infinity is a concept that is universal, or unchanging. Infinity is always infinity.

Well in other words of course, but I think differently. You cannot just say infinity is the biggest number you can think of times 100,000,000 and plus 1 but more. Because, like you said, there is infinity between 1 and 2. Cantor believes in pairing though, you should check out his theories and maybe read most of what has been posted--it has been mentioned a couple times. Don't blame ya for not seeing it though, there are quite a few pages of text now.

reply to post by athes


Well equilibrium in environment makes sense... But then really, zero would represent order, lack of entropy. I know the universe favors chaos, yet I still fail to believe that it cannot be attained.

Hmm, I think I can grasp infinity divided or multiplied by a number, but the OPs question, of 1 divided by infinity, I am struggling with. 1 divided by anything more than zero gives less than 1 right? a fractional number. And 1 divided by infinity? Seems it would be more than zero but less than one of something.