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

reply to post by OutKast Searcher


A couple of things I would like to say...

1 I am going to bed due to sleep deprivation so I will not quote anything. I need to say this tonight while it is fresh in mind

2.Yes, I did mean infinity, not zero--dumb mistake
3. If we treat infinity as a number (you and I agree that it is not, but I do think that it can act like a number to a degree) and actually reach it, a limit still exists. If I asked you the limit as x->4 in y=2x, the limit is 8 even though that point clearly exists and is reachable.
4. Base 10 is how math ends up being processed in today's society, thus we play by its rules. If I asked you in base three I am sure I could find some fraction there that does not work out properly and provide a similar proof, in which case I gave you a proof of basic math which you appear to want to break, and me breaking your basic un-numerical math concepts are moot.

5. With that being said, I love your example of the line with length of 1, very good point.

6. You can divide by zero, it happens all the time. With l'hopital's rule it is always welcomed in concept. Also this, idea of not dividing by 0 comes back to infinity not being able to be reached--mere speculation that cannot technically be proven nor disprove except through more concept and speculation. SO for our purposes in the original thread, we assume it CAN be.
7. As for some of the other good points you mentioned, again we are assuming that infinity is one concept with (1) quantifiable summation. I still believe some infinities can be larger than others (by reaching the plane of infinity faster than other infinities)

8. sinx/x evaluated at 0 produces an indeterminate (infinity) so it is difficult to say that this example really works. Yes the limit does not correspond with the "plugging in" of 0, but it produces something else that could mean many different things (theoretically even 1, who knows)

9. Sorry this is choppy and perhaps incohesive. I am tired and any things you wish to point out that do not make any sense I will attempt to explain tomorrow.

10. Thanks for your input, at least you stand by what you know (even if you know I am making at least a wee bit of sense).

reply to post by circlemaker


Wow, finally someone thinks outside the box! I wish for you to greater explain the picture for me if possible. I think that every number must be a limit because by saying something equals 1 you are also saying that it is exactly one, or 1.0r. That is just as infinite as 10r, or however you wish to define infinity. every number is a representation of an idea, and respectfully infinity is the same way--just less quantifiable.

Originally posted by circlemaker
reply to post by OutKast Searcher

 

Anything / infinity = 0, except infinity. It's hits the limit. In this sense "limit" is used in it's proper context but I still say infinity's a number. I think any number can be treated as a limit. I've seen how 1, the square root of 2, the square root of 5, and phi are also limits (or mirrors as I like to call them). Oh yeah and there's 0.

edit on 3/19/2012 by circlemaker because: edit to add 0

So anything/infinity = 0?

So:

1/infinity = 0

2/infinity = 0

This means

1/infinity = 2/infinity

Which means

1 = 2



This is the problem with using the concept of infinity as a number...you are creating a paradox.


How do you resolve the above situation?

reply to post by OutKast Searcher


Has to do with rates is my guess. You cannot just multiply each side by infinity to resolve that 1=2.

Ok seriously, last post of the night, more tomorrow

Yeah I have to agree with the person who recommends looking at applied mathematics especially considering you're going under a physics adept name.

Quantum physics changes everything about infinity due to non-commutative properties of time.

So (A x B) - (B x A) is greater than zero in quantum mechanics.

You're talking about an asymptote that assumes the commutative property.

It's very easy in math to overlook very basic assumptions.

Time is not a spatial measurement for one thing -- this is an assumption of the commutative property.

So consider de Broglie's Law of Phase Harmony -- due to relativity when energy frequency increases then time slows down and expands in value -- this is a contradiction since time is the inverse of frequency. De Broglie argued the only way this is possible is that when frequency is zero then time as phase is infinite so there is a phase velocity that is superliminal as an information signal. This infinite phase then is a reverse time due to the curvature of space and it is an "internal" time in contrast to the external group phase velocity of the particle being measured. The two are coherent in phase.

Quantum physics is the foundation of physics and so it should be taught first before classical physics -- this is what quantum physics Professor Herbert Bernstein states.

Zero to infinity: the foundations of physics That's the google review --

Basically there is no "pure" mathematics -- and there are inherent paradoxes in set theory that remain unsolved -- as discussed by math professor Luigi Borzacchini. So the technology used to measure time inherently limits the measurement due to time-frequency uncertainty and this is actually found in the foundation of mathematics coming out of music theory -- as Professor Borzacchini details -- in the paradoxes of incommensurability and the continuum.

This means that the foundation of math is actually philosophy and not any physical measurement using technology. Whereas commutative math assumes the technology provides a "pure" or objective measurement.

Obviously you need to get an education -- but please don't think it is a "pure" education -- it's instead a technical training. If you want a real education into infinity then you need to study a deeper level of philosophy.

I do not know if someone has mentioned this yet, and I hope it is not off topic. Sorry for my ignorence before hand. Also, all of you folks who know alot about math please correct me, I have no idea if this is even going to make sense. For anyone like me who is kind of a dunce when i comes to math and reading this topic the following might help. This is how I taught myself math, and it got me 100s on all my college tests, so it might help. I think it is handy when thinking about things like infinity.
First imagine you have some objects, lets say marbles. Now if you imagine a space, lets say a circle on the ground, and there are no marbles in the circle, you have zero marbles in the circle, but if you place a marble in the circle, you now have 0+1 marbles, or one marble. Then if you place another marble in the circle you have 1+1 marbles or the circle contains two marbles. Basic addition, subtraction being opposite obviously.

Now, lets say that that circle contained three marbles. you have 1 circle containing three marbles. but if you were to add two more circles containing three marbles, you would have 3*3 , or nine marbles. In other words, you have three groups of three marbles. So, the first number is the number of objects in the group and the second number is how many groups total. So multiplication is more or less the same as addition. So addition and subtraction deal with objects as idividual units, while multiplication and division deal with objects as groups, in a basic sense. So zero multipied by infinity would be the same as adding emtpy groups together to measure the total contents, which would be nothing, as they were empty, but we know that 1 multiplied by a number, is that number, so 1 multiplied by infinity is the addition of an unspecified continuing number of groups containing one, or a circle containing 1 marble + a circle containing 1 marble + a circle containing 1 marble... etc.

I know that is just basic math, but really whether dealing with parts of an objects as the individual objects, or whatever, the principles remain the same. Of course that is assuming all objects or parts are exactly the same, but if they are not, then stuff starts getting pretty cool, but I don't feel like getting in to that because it is difficult for me to explain it well in text.

One thing I have noticed, is that infinity does not require a cause, it could have one but it is not required, it simply is infinity, so any point within infinity is represented. I don't know, I think I just confused the other people like me who do not know much about math. I guess what I am trying to say is that infinity is potentially anything but already something. I wish I could describe how I am right now picturing it in my mind, then it wouldn't sound so stupid. Infinity is all possibilities, and at the same time it is only one. While the human mind can think about it, machines currently have their limitations, and so calculating something that is everything, but also only one thing, makes it seem like there are paradoxes, but really, there are not.

Also, I mean in math, even if it doesn't sound like I am talking about math. I appologize if I got confused, I am really sleepy, and I do not remember terms very well, so I always forget hwo to say what I mean when talking about math, anyway I hope my post was relevant, I think when dealing with concepts such as infinity it is helpful to reduce it to absolute basics, and then imagine it as something concrete, to help it not become maddening.

Originally posted by OutKast Searcher

Originally posted by circlemaker
reply to post by OutKast Searcher

 

Anything / infinity = 0, except infinity. It's hits the limit. In this sense "limit" is used in it's proper context but I still say infinity's a number. I think any number can be treated as a limit. I've seen how 1, the square root of 2, the square root of 5, and phi are also limits (or mirrors as I like to call them). Oh yeah and there's 0.

edit on 3/19/2012 by circlemaker because: edit to add 0

So anything/infinity = 0?

So:

1/infinity = 0

2/infinity = 0

This means

1/infinity = 2/infinity

Which means

1 = 2



This is the problem with using the concept of infinity as a number...you are creating a paradox.


How do you resolve the above situation?

0*1 = 0. 0*2 = 0. This works fine too. There's no paradox. Think of numbers in terms of distance from the origin (typically 0).

If you divide any finite number an infinite number of times, the resulting length or distance (from 0) is still 0.

An infinite number can't be divided by a finite number. One has polarity, the other doesn't. So what happens is the result collapses to one of the non-polar limits (either 0 or inf).

0*inf is unique because they're both non-polar, so they result in creating a new limit in the form of +/-1.

Originally posted by PhysicsAdept
reply to post by circlemaker

 

I wish for you to greater explain the picture for me if possible.

It's what I call the "root grid". I discovered it while looking for connections between circles and square roots. That link is an expanded reference to the link in my sig which is a tool I created to better understand math. There's too much info to post it all here.

Infinity is defined as the concept that no matter what number you write down, there is always one bigger. There is no arguing that you can reach it somehow. That is why it usually isn't used much outside of limits in calculus or when a 5 year old is trying to win an argument. With that in mind, it doesn't matter if you are dividing 1 or 1 million by it with respect to limits because eventually the function approaches 0, which we call the limit since the value never actually reaches it.

And for those of you who think .9 repeating (.9 with a bar over it) doesn't equal 1, it can be proven using infinite series:

.9999999..... = .9r = 9/10+9/100+9/1000... = (9/10)*(1+(1/10)+(1/100)...)

= (9/10)*(the sum from n=0 to n=infinity of (1/10)^n)

Now consider (the sum from n=0 to n=infinity of (1/10)^n). It is a geometric series, which in general terms is

(the sum from n=0 to n=infinity of r^n)

For a geometric series with 0 < r < 1, the series is equal to 1/(1-r)

With r = 1/10, this is 1/(1-(1/10)) = 1/(9/10) = 10/9

I.E. (the sum from n=0 to n=infinity of (1/10)^n) = 10/9

substituting, (9/10)*(10/9) = 1 = .9r

I apologize, I couldn't think of a good way to use sigma notation, or find the infinity or repeating symbols, but you should be able to get the gist. Also I provide proof for the geometric series here.

Whoever mentioned that it would be covered in college was correct at least in my case, but it was in Calc II, not my first semester.

Infinity is a rational number.
You can never use it in multiplication or division with any other number and get an integer result, including zero (0)
Thus, 1/infinity is asymptotic. It approaches zero (the limit as stated earlier) but can never get there.

reply to post by PhysicsAdept


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.

forgive me, I haven't had time to read the whole thread but it caught my eye because of this fantastic documentary I watched last week, on infinity. Also touches on calculations using infinity towards the end.
not sure if people outside the UK can access this but give it a try

www.bbc.co.uk...

reply to post by PhysicsAdept


One divided by infinity equals...

Zero decimal followed by infinity with a one on the end

I'd like to point out that infinity is not a number but a concept of a loop. You can't really do math calculations with it because it is a concept not a number.

Originally posted by PhysicsAdept
reply to post by OccamAssassin

 

Here's a question I have wondered for a while... What is the purpose of other bases? I mean I know that we use decimal and it works out nicely because I am used to it, then base 2 is used for computers... probably because analogue things works off of a system similar to binary I am guessing, then there is hexadecimal. I don't know exactly the these bases are used instead of the others, but I am really curious to how the other bases benefit the world, what are the other bases even used for?

Binary is useful with computers as it is a very good way of representing 'on' and 'off' states or 'true' and 'false' - basically everything you see on this page is represented with these two states in your computer's hardware.

Hex is also useful in the computing space - e.g a property of Hex is that it allows large numbers to be written with a few characters - which is in turn utilized to address a large memory space in a relatively simple way ...

I must say you've lit up an old flame with the sparks of this thread I will definitely embark on a math refresher - just like you mentioned above, calculus used to be one of my favorite topics also .

Hi there,


In mathematics "infinity" simply means a set of numbers that are "without limit." While you can write a symbol down on a piece of paper to represent the concept of "infinity" just like you can write down the number "2" to represent the concept of "two," do not confuse "infinity" with a finite set of numbers. With a finite set of numbers, one can apply the basics of computation (e.g., addition, subtraction, multiplication, etc etc.). This can not be accomplished with an infinite set of numbers.

While it is true that the set of numbers between 1 and 2 is infinite and while the set of numbers between 1 and 3 INCLUDES the set of numbers between 1 and 2, it is NOT TRUE that the set of numbers between 1 and 3 is LARGER than the set of numbers between 1 and 3. The concept of "larger" can only be used when comparing two FINITE things. Make sense?

Its like you're asking what color a perfectly transparent window pane is. Since color really refers to the perceivable light waves reflected off a surface, the concept of "color" doesn't apply to surfaces that do not reflect light.

You may find this concept a bit troubling at first; but, it'll grow on you and you'll begin to see certain concepts with more clarity. Many of life's more "difficult" questions are simply a misuse of language.

Do a Google search for "Georg Cantor," if you haven't already. He wrote a lot on the topic of infinity - but PLEASE pay close attention to how he defines certain terms. Many times Cantor uses a word to mean a very specific thing but that same word may be used differently by others when writing/discussing the same topics; this is what leads to much of the confusion.

That being said, keep in mind that I may have no idea what I'm talking about and that you're going to develop theories that will revolutionize number theory. Give Cantor's works a read, keep in mind what he means when he uses specific terms and be open minded to all possibilities.

Hope that helps.

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.

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?

Nice and deep topic, very good!

This post reminded me of a physics/religion conversation/debate my wife and I had with my late father.
While contemplating the edge of the known universe, he used the value of infinity.
I like to argue for a better definition than: Infinity=I don't know.
He just kept yelling:
"GOD IS INFINITY!"

I asked him to define both, at witch point he was stuck in a loop saying "Infinity is god".

His complete lack of logic (or jump of logic) really surprised me, for an educated man with many physics classes under his belt. I suppose there was alcohol involved, so.....

I would like to officially define infinity as:
The most you could imagine times 65.25 bazillion. The resulting number does not equal god.
Seems just as accurate as any definition for infinity, don't you think.

Carry On!

reply to post by CaptGizmo

I think you meant oneteen. Eleven originates from the Germanic "ainlif" which literally means "ain" - one and "lif" - left over. In the context of numbers it reads as "one past ten". The same goes for twelve, read "two past ten".