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

reply to post by djeminy


Right, using the halving method we would still always have a piece. It would be getting ever smaller, but not quite 0.

However I have considered a way to "reach infinity" conceptually.

In the image the circle's radius is 1, so pi is a half circle. It's divided by 10. The dividing lines end at the tangent. But when the dividing line is completely horizontal, it's assumed that the line extends to infinity (there's nothing else it can be). It only works with even number divisions.

Originally posted by PhysicsAdept
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?

Absolutely!
I agree with you 100% x ∞! Lol!

Seriously, yes, I think the infinity concept can sometimes be all inclusive as you suggest. Think of the resulting sums from a random number generator.
I think it has to be viewed as a concept, and an admission that it is an unknown quantity.
So to quantify anything with infinity, is only to say at is a large value of an unknown amount.
I think human scientists prefer to use the word infinity, in lieu of "We have no idea".

I would say infinity is the "gray area", the "unknown". ∞ / ∞ is not a valid formula.
However, the number of grains of sand in Miami alone, can never equal zero.

Originally posted by PhysicsAdept
reply to post by djeminy

 

If ∞ has no affiliation with numbers what so ever, then tell me what 1/0 is. To say that it is undefined is only one narrow aspect to the situation... 0 in theory would go into 1 an infinite number of times. AND the slope for a vertical line does not only approach ∞ in the limit, but also most logically meets it.

Then again, all of limits must also be useless because ∞ does not involve any numbers whatsoever...?

You can have an unknown amount of numbers,

and you can have an unknown amount of limits if you like,

but this has nothing to do with 'infinity' or 'eternity'.

Cheers

Originally posted by Wookiep

Originally posted by OutKast Searcher
reply to post by Wookiep

 

You can prove faulty reasoning and the incorrect use of concepts.

But if you are Physics thinks the reasoning is sound and concepts are valid to use as numbers...I would love the answers to these.

1/large = ?

1/small = ?

1/huge = ?

1/finite = ?

Oh good luck with that. If you can't grasp the ideas that you obviously disagree with as CONCEPT and THEORY and QUESTIONING then you don't belong here. I don't believe the answers to this "reasoning" as you put it were claimed to be solved by the OP. You're asking the question to provoke and troll, period. Go troll somewhere else until you can add something valuable rather than circular arguments that you think pertain to the OP, but don't.

edit on 20-3-2012 by Wookiep because: (no reason given)

Hi Wookiep,
Don't be bullied.
Anyone that wants to understand infinity can only do it in a circular way.
There are no way points.
Math is just a tool developed by mortals. Infinity is a concept. All be it developed by same.
Ask all the questions you want and give all the examples you want.
help deny the IGNORANCE
ljb

Originally posted by circlemaker

Just for comparison, here's a visual model of halving method using radians.

Originally posted by djeminy

Originally posted by kykweer
reply to post by PhysicsAdept

 

If u split an apple in half, and split half the apple in half and half of half then half of that half to infinity... Will there eventually be zero apple left?

No. You'll never be able to get rid of the apple that way.

And of course you don't need to split the apple in half first.

just take a tiny bit of the apple and start splitting this apple

part in half from there on; as sooner or later you would have

reached this point anyway, had you started from scratch!

Cheers

Well if you can't get rid of the apple, then...

1/infinity >0

1/infinity would equal "as close to 0 as possible."

Originally posted by kykweer

Originally posted by UKLionheart

Originally posted by PhysicsAdept
reply to post by UKLionheart

 

Would you say then, that .000000000000000000000000000000...1 equals 0?

Hahaha. No, because you can't have infinite 0 before the one. As soon as you put that one on the end, it is no longer 0., but with 0.999 going off into infinity, that's different!

Here's the proof of the0.99999 recurring thing:

Let's call x = 0.99999 recurring.

10 x= 9.999999 recurring

deduct x from both sides:

9 x = 9 therefore x = 1

therefore 1 = 0.9999 recurring.

Tralahhhhh!

The question isn't the math, its a logical question in relation to infinity as infinity is more or less an absolute value. So 10 times infinity minus infinity is a contradiction as 10 times infinity equals 1 infinity equals 2 million times infinity.

Again subtracting infinity from infinity is like subtracting a chicken from a horse.


Because 10x - x = 0.999r - x

9x = x (infinity stays the same at a given point in time)

Therefore infinity = infinity
Tralahhhhh!

Hasn't that crap formula been debunked like hundreds of time? Gosh I swear its like nibiru

edit on 20-3-2012 by kykweer because: (no reason given)

edit on 20-3-2012 by kykweer because: (no reason given)

Infinity is not an absolute value, and never can be; it is a concept. You cannot use it as a number to "debunk a crap formula" and no, it is not a debunked crap formula anyway, because it is the basic conversion of recurring decimals to fractions algorithm. The beauty of Maths is that once something is proven, it can be written in stone, which is why we still use quadratics based on the Mesopotamian completion of the square, and Greek proofs from Euclid's Elements etc.

Plus, please show me anywhere in my "debunked crap formula" where I have multiplied infinity by 10???

Like infinity? Love pi!

3.141592653589793238462643383279502884197169399375105820974944592*640628620 8998628034825342117067982148086513282306647093844609550582231725359408128481117 450284102701938521105559644622948954930381964428810975665933446128475648233786 783165271201909145648566923460348610454326648213393607260249141273724587006606 315588174881520920962829254091715364367892590360011330530548820466521384146951 941511609...




Edit:

Baaaah there's an error in that number... must have been some govt agent man afraid of pi people

I love how all you geniuses are coming in here saying how infinity can't be used as a number while I've been using it as a number the past few years just fine. There don't seem to be very many out of the box thinkers in this area, even here on a metaphysics forum where I'd expect more open-mindedness.

There was a time when 0 wasn't considered valid. There was also a time when "imaginary numbers" were mocked.

From wikipedia:

Prior to the concept of negative numbers, negative solutions to problems were considered "false" and equations requiring negative solutions were described as absurd

Although Greek mathematician and engineer Heron of Alexandria is noted as the first to have conceived these numbers,[2][3] Rafael Bombelli first set down the rules for multiplication in the complex numbers in 1572. The concept had appeared in print earlier, for instance in work by Gerolamo Cardano. At the time, such numbers were poorly understood and regarded by some as fictitious or useless, much as zero and the negative numbers once were. Many other mathematicians were slow to adopt the use of imaginary numbers, including René Descartes, who wrote about them in his La Géométrie, where the term imaginary was used and meant to be derogatory.

Even Descartes with all his insight didn't get it. How long until infinity is recognized as valid?

Originally posted by PhysicsAdept
reply to post by MeesterB

 

So then at infinity, would it not equal 0?

I mean, at a very large number it would equal close to zero but we are not talking about a number at all. We are talking about a concept. So then conceptually, would not 1/∞=0?

I don't think this is something that can be over-thought, but I do think that there is some answer out there that will make it more clear...

Actually you hit the powers of ten a nasty blow.

If you take a chicken that is running round in figure eights with a mouth full of oranges and predict the exact location where it will deficate, then divide that by the number of remaining oranges c^.= multiply that by s compareable negitive tangent and you know you have solved the triangular dicection theory.
Sorry if my spelling stinks.

reply to post by circlemaker


Right. Descartes had stumbled upon imaginary numbers by contemplating (-1)^(1/2).

He himself had doubt in their practicality, but now look. Ever heard of alternating circuits?

Michael Faraday discovered alternating current around 1830, and imaginary numbers are used in electrical engineering. (of course, there an imaginary number is denoted with j instead of i because i stands for electrical current )

Haha, PS the link is to mathisfun... It is very elementary but easy to understand (it is harder to refute the basics sometimes )

reply to post by circlemaker


Care to enlighten us with a proof involving infinity?

reply to post by longjohnbritches


Could you explain? I do not quite get where you are getting at...

reply to post by OccamAssassin


This is a bit off topic in a way I suppose... But can you prove there is wind, even though there are no equations to define it?

Originally posted by PhysicsAdept
reply to post by OccamAssassin

 

This is a bit off topic in a way I suppose... But can you prove there is wind, even though there are no equations to define it?

How about with a windsock?

There are actually many (many) equations to quantify the wind. Without them we would not have been able to optimise powered and non-powered flight vehicles.

I would start by checking out fluid dynamics.

reply to post by OccamAssassin


Well there are so many variables, and with something like a fluid there are less I would assume. I mean I know a big topic in engineering is wind because though we have wind-powerable sources and turbines that can move depending on from where the wind id hitting but we have no real exact equation for wind. We cannot predict wind yet to a tee enough for wind energy to be t peak efficiency. I mean, wind is more than just a concept but we can assume there is some equation for wind. It has been around since man has been around, and yet there still exists no quantifiable evidence of a uniform equation...

As far as I know anyway. Just interesting to ponder. We know it exists and we even use it to our advantage--yet no equation. I figured infinity is (more or less) in the same boat.

Don't get me wrong, I know there are the Bernoulli principles, but will it helps demonstrate a concept. Is there an equation for actual wind? Like if I had a gust of wind coming toward me, are there equations to find the wind power at a point, and pressure differentials beyond averages? Just wondering.

INFINITY is best described as a process. For example +1 you can add 1 to a number to infinity. To see how infinity really works in the real world take a look at pi. The number goes on forever . The reason is simple, take the basic equaliteral trinagle (with a radius of 1 unit) and add one side to it to make a 4 sided regular polygon (square) and then again for a 5 sided regular polygon. What you get when you do it an infinite number of times is a circle. Now if you do the maths and start from working out the perimeter of each shape, you start to get Pi . This is why Pi has no end because you can always add another side to make another regualr polygon.

reply to post by OccamAssassin


I mean (and I say it very loosely) infinity exists IMO because we are so sure of zero's existence...

reply to post by minor007


I agree! A circle, is a bit of a limit. If n equals the number of sides of a shape, then as n-> approaches infinity then we get closer and closer to a circle. So I think because everyone is so sure a circle exists, then we must all argee that infinity does as well.

Now there are people on this forum that would say that there is no such thing as a true circle--there may be a shape with 100458745873548 sides, but it is no circle. I can see that in reality, however as concept I see nothing wrong with a circle, nor do I infinity. I believe that at some point, perfection has to exist. An atom? Is it perfectly circular? Would that not prove infinity in some aspect?