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

reply to post by PhysicsAdept

So then at infinity, would it not equal 0?

You can't arrive "at infinity" - if you could it would be finite, wouldn't it?
If you divide something infinitely, you get infinite segments, not "nothing".

Think of it as a decimal with an endless string of zeroes, with a "1" at the end that you'll never reach.

Originally posted by OutKast Searcher
reply to post by circlemaker

 

That's completely nonsensical. Both sides of what?

You're treating infinity as if it's a finite (but very large) number with polarity. It doesn't work like that. I've already explained how this works but you claim that a finite number can't be divided an infinite number of times and that's where you stopped thinking.

I agree...it is completely nonsensical...all caused by you claiming anything divided by infinity equals zero.

I am not treating infinity as anything...you and the OP are trying to treat it as a number that you can use mathematical operations on.

YOU say that:

1/infinite= 0

Well what is the answer to this:

1/finite = ?

or

1/large = ?



YOU are treating a concept (infinity) as a number...and I'm telling you that you are wrong. I'm showing you are wrong by the paradoxes it creates. And yet you are saying that is is ME that is using infinity as a number and that is non-sensical....we seriously just went in a complete circle.

Correct.

1/infinity = 1/infinity.

2/infinity = 2/infinity.


1/infinity = 0, is nonsensical.

0 can never become 1, and 1 can never become 0.

1 will always remain 1, and 0 will always remain 0.

And so on!

Cheers

Re-posted here from the "Limits at infinity, the number 1 ......" thread, as that thread is 'sinking' quickly!



(reply to post by OutKast Searcher)


OKS is right of course. One cannot use mathematics to define the infinite.

And of course one cannot bisect 1 or any other unit in such a way that they

become something else entirely. Thus all rational numbers between 0 and 1,

even if one 'create' infinite amounts of rational numbers, will all be a product

of 1 exclusively.

Naturally, 0 is infinite within, of and by itself, and can therefore never be

defined by mathematics, but must solely be explained in a spiritual sense.

Spiritually, 0 is related to the circle which also only can be defined in this

way.

To attempt initially to define the circle, a new Axiom must be used and which

simply states:

THE INTERSECTION OF TWO CURVES CAN NEVER CREATE A POINT.
ONLY WHEN TWO STRAIGHT LINES INTERSECT CAN A POINT OCCUR.

This again will prove that one cannot bisect the circle to determine the constant

by which the circle can be measured, but must use other ways to do this.

Knowing that the 'circle' is simply a product of vibrations, oscillations and

wavelengths etc., and not the other way around, the circle must be treated in

the same way as these various manifestations.

The true and correct pi is of course not irrational, but based upon a rational

number which is 22/7 or 3.14285714285714....... repeated ad infinitum.

This can now be proven beyond doubt to any free-spirited honest person

not zealously burdened down to any 'belief system' or 'dogma'!

All irrational numbers are man-made, and as such has no lasting benefit

to anyone.

Phi and all square roots are all products of natural numbers, and therefore

also those too, should be deemed rational numbers ......if any true justice

any longer exist in this world!

Cheers

Originally posted by ClydeFrog42
reply to post by PhysicsAdept

 

This has got to be one of the dumbest threads i have ever read.

Infinity is not a number. Therefore, subbing it into algebraic equations is completely useless.

Infinity is a concept. You cant divide a number by a concept...

1/infinite = nothing (not zero... nothing)

This is pretty basic 11th grade logic. Im extremely surprised to see 2 threads like this on the front page within 2 days.

only on ats, i suppose

Roll your eyes all you want. All you're doing is regurgitating what other people have told you. Just because some teacher says that's the way it is doesn't make them right.

If someone gives you a non-answer, it's because they're not trying hard enough. Take 0/0. People say it's "undefined". Meanwhile I came up with "shadow numbers" to explain it.

I'm surprised at how many people think that the current level of mathematics is sufficient. From where I'm standing there haven't been many innovations in math since Pythagoras. People like you act as if we know everything there is to know about math. We don't. It's infinite, and there's an infinite amount of potential new discoveries still awaiting us.

0 is officially considered a number yet infinity isn't. This is preposterous. Just try counting to 0 from 1 in fractions. 1/1, 1/2, 1/3, 1/4, etc. You won't ever get there. Invert the fraction and you have the whole numbers counting to infinity: 1/1, 2/1, 3/1, 4/1... The fractional part is usually removed when we count due to redundancy, but the truth is that 0 is just as far from 1 as infinity.

Originally posted by OutKast Searcher
I agree...it is completely nonsensical...all caused by you claiming anything divided by infinity equals zero.

Nice deflection. You didn't even bother to answer my question.

reply to post by circlemaker


lol.... yes, the number one can be divided into an infinite number of fractions......... hence the concept "fractions". You know, like, when you split something in two?

We use the concept "infinity" to describe this phenomenon.

That has absolutely NOTHING to do with the FACT that infinity is a conept, which has absolutely no use in any algebraic equation, and the plain and simple FACT that the original post is flat out WRONG.

As are you.

This is plain to see for anyone with so much as an ounce of common sense. Im not sayin... im just sayin, is all.

Originally posted by circlemaker

Originally posted by ClydeFrog42
reply to post by PhysicsAdept

 

This has got to be one of the dumbest threads i have ever read.

Infinity is not a number. Therefore, subbing it into algebraic equations is completely useless.

Infinity is a concept. You cant divide a number by a concept...

1/infinite = nothing (not zero... nothing)

This is pretty basic 11th grade logic. Im extremely surprised to see 2 threads like this on the front page within 2 days.

only on ats, i suppose

Roll your eyes all you want. All you're doing is regurgitating what other people have told you. Just because some teacher says that's the way it is doesn't make them right.

If someone gives you a non-answer, it's because they're not trying hard enough. Take 0/0. People say it's "undefined". Meanwhile I came up with "shadow numbers" to explain it.

I'm surprised at how many people think that the current level of mathematics is sufficient. From where I'm standing there haven't been many innovations in math since Pythagoras. People like you act as if we know everything there is to know about math. We don't. It's infinite, and there's an infinite amount of potential new discoveries still awaiting us.

0 is officially considered a number yet infinity isn't. This is preposterous. Just try counting to 0 from 1 in fractions. 1/1, 1/2, 1/3, 1/4, etc. You won't ever get there. Invert the fraction and you have the whole numbers counting to infinity: 1/1, 2/1, 3/1, 4/1... The fractional part is usually removed when we count due to redundancy, but the truth is that 0 is just as far from 1 as infinity.

You forget that all the individual fractions in sequence on both sides of 1, when multiplied with each other,

reverts back to 1 or unity. Zero plays no part in this.

Cheers

reply to post by circlemaker

Take 0/0. People say it's "undefined". Meanwhile I came up with "shadow numbers" to explain it.

I request a thread be made on "shadow numbers".

Maybe I'll present my counter argument of "invisible numbers".

From where I'm standing there haven't been many innovations in math since Pythagoras.

There was this one guy named Newton...but nah...he wasn't very important.

0 is officially considered a number yet infinity isn't. This is preposterous. Just try counting to 0 from 1 in fractions. 1/1, 1/2, 1/3, 1/4, etc. You won't ever get there. Invert the fraction and you have the whole numbers counting to infinity: 1/1, 2/1, 3/1, 4/1... The fractional part is usually removed when we count due to redundancy, but the truth is that 0 is just as far from 1 as infinity.

Oh boy...I see you have completely confused yourself. Which is why self teaching isn't the best way to learn something.

Apples have been popular in these threads. There is one apple in a box...then somoene takes it...how many apples are in the box? That's right...zero.

Zero was a mathematical breakthrough.

Infinity is as well...but as a concept on a boundless set...not a number.

Originally posted by circlemaker

Originally posted by OutKast Searcher
I agree...it is completely nonsensical...all caused by you claiming anything divided by infinity equals zero.

Nice deflection. You didn't even bother to answer my question.

It's not a deflection...it's the truth.

I don't have time to teach you basic algebra...sorry.


I'm still waiting on an answer from you on what is 1/finite?

Originally posted by Sly1one
reply to post by PhysicsAdept

 

Personally, I don't think you understand the concept of infinity.

Now, the question is: what happens to 1 when it is divided by infinity? Well you can look at it graphically in the example of y=1/x, and take a look at the limit of y when x approaches ∞. Well, you end up realizing that the limit is zero.

how can anything "approach infinity"??? how do you know you are there? You can't...there is no approaching anything in infinity...its like traversing a circle, you will never get to the "end" and it doesn't matter where you start as start/end are man made points of reference to quantify something for measurement. Start/end in the objective sense doesn't exist...unless you the person decide to assign points to something and that is all your imagination at work.

1 is a man made concept/digit...it doesn't truly exist anywhere. Go find me "1" of something...once you think you have I'll show you more, or divide it and call it another digit....

give me 1 apple ill show you an apple tree, give me one rock ill show you a beach, give me 1 sun, ill show you a galaxy, give me 1 galaxy ill show you a galaxy cluster, give me a galaxy cluster and ill show you the universe...

1=∞
in which case your equation would read as such:
∞/∞=∞

Wow, you don't seem to understand anything. Let me illustrate what "The limit of 1 over x as x approaches infinity = 0" means:

1 divided by 2 means what measure do 2 things have to be to equal 1? Answer is 0.5

1 divided by 20 means what measure do 20 things have to be to equal 1? Answer is 0.05

1 divided by 200 means what measure do 200 things have to be to equal 1? Answer is 0.005

1 divided by 20,000 means what measure do 20000 things to to be to equal 1? Answer is 0.00005

1 divided by 2000000000000000000000000000000 means ... answer is 0.0000000000000000000000000000005

You see, the idea of this process is represented by limits. As this continues on, as we *approach* infinity (as our number gets larger in larger), the answer approaches zero.

The entire idea of what I just illustrated can be written as "The limit of 1 over x as x approaches infinity = 0".

You see, the idea of this process is represented by limits. As this continues on, as we *approach* infinity (as our number gets larger in larger), the answer approaches zero.

reply to post by WhatAreThey


You are making the false assumption that infinity is something that can be "approached". As if you keep dividing forever you will hit infinity and zero at the same time....

This is fundamentally flawed logic. You can divide as long as you want, you will never reach zero, nor will you ever (even if you divide the number 1 in half using a supercomputer for the rest of time) reach infinity.

Maybe its convenient to believe that you can "approach" infinity, but infinity is unapproachable. It is a concept used to describe something that has no limits... so it makes no sense to use infinity to describe limits...

Literally senseless. You are treating infinity as if it is a certain value that can be attained. It is not.

Originally posted by ClydeFrog42

You see, the idea of this process is represented by limits. As this continues on, as we *approach* infinity (as our number gets larger in larger), the answer approaches zero.

reply to post by WhatAreThey

 

You are making the false assumption that infinity is something that can be "approached". As if you keep dividing forever you will hit infinity and zero at the same time....

This is fundamentally flawed logic. You can divide as long as you want, you will never reach zero, nor will you ever (even if you divide the number 1 in half using a supercomputer for the rest of time) reach infinity.

Maybe its convenient to believe that you can "approach" infinity, but infinity is unapproachable. It is a concept used to describe something that has no limits... so it makes no sense to use infinity to describe limits...

Literally senseless. You are treating infinity as if it is a certain value that can be attained. It is not.

No, he is absolutely right in his description of the limit function.

And you can "approach" infinity...but you can never reach it.

For 1/x as x approaches infinity, the answer approaches zero. X will never reach infinity, and the answer will never be zero. This is the whole point of the limit function...to find the limit.

Originally posted by OutKast Searcher

I request a thread be made on "shadow numbers".

Maybe I'll present my counter argument of "invisible numbers".

No need for an entire thread. Count from infinity instead of 0 and you're dealing with shadow numbers. From 0's perspective they're all collapsed to infinity. From infinity's perspective all the numbers which use 0 as their origin are collapsed to 0.

Instead of offering non-answers I actually figure stuff out.

Here's a picture showing shadow numbers next to the "real numbers". The awareness barrier defines the numbers we haven't counted to yet, hence the name.

reply to post by circlemaker


You still haven't answered what 1/finite is.

You seem to be dodging that.

Originally posted by OutKast Searcher
reply to post by circlemaker

 

You still haven't answered what 1/finite is.

You seem to be dodging that.

What the hell are you talking about? What's 1/finite? Did you mean 1/infinity?

Originally posted by circlemaker

Originally posted by OutKast Searcher
reply to post by circlemaker

 

You still haven't answered what 1/finite is.

You seem to be dodging that.

What the hell are you talking about? What's 1/finite? Did you mean 1/infinity?

No, I meant 1/finite.

You seem to think you can divide by the concept of infinity.

So what is your answer to dividing by the concept of finite or finitude if you want to be technically correct.

reply to post by OutKast Searcher


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

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...

But infinity will be a number at some stage, so if infinity was a number x, 1/x won't equal zero.

If infinity could be equal to horse on the other hand or an external concept to a number then you may have a point.

I don't understand your argument though, is it philosophical or logic?

Logic states that it will become very very very close to 0, but not quite it.

Philosophical: "well it'll be so close, let's call it zero, I believe it will eventually get there"

So what?

Can you devide any number by 0 and infinitely?

X/0=infinity?

I mean really, don't we have better stuff to think about?

reply to post by PhysicsAdept


I am in college currently and have been through Trig / Cal 1 and 2. Chemistry i avoided , hate it.

Mathematics are ever-changing. There is no set rule of Infinity. Basically what we have learned is ... they don't know nothing about anything. They just guess and say its right. (Introduction to Theoretical Physics and expressions - i took this class because it was more of a philosophy class about the world of mathematics , physics and theoretical algorithms - you don't do a lot of math , you simply discuss the formula / algorithm)

You can creat algorithms for anything in known existence. However , our current formulas for understanding the world around us is in constant change due to the expansion of the universe and do the string theory. Basically , Mathematics is nothing but a Human interpretation of the world around us.

Infinity expresses what we do not know. There is no formula for it , because it express all ideas in mathematical numbers that are unknown. Infinity is simply the unknown.

------
Basically you should be looking at the world around you , and begin to study Quantum Physics. Quantum Physics is basically the cycle of infinity. Such as two things existing in one dimension at two separate locations at the exact same time.

Vibrations and Frequencies are the strangest things i have learned about in College. Basically using certain frequencies will solve all of man kinds problems while at the same time ensuring its destruction. It's very hard to explain this. Frequencies also relate to infinity due to the infinite range of possible frequencies creating an infinite number of expressions (good or bad) which can be solved through the spectrum of sound (for better or worse).

You could break down Atoms to infinite amount of "smallness" meaning an Atom can be the biggest thing in the universe , wait a minute ... WHATTT? Yeah , you read that right.

-----

What is Infinity? The unknown. Nothing more - regarding expressions.

-----

The philosophical point of all of this? Is that infinity is the expression of God.

-----

Infinity cannot be applied. You must constrain infinity to solve a finite problem and this finite problem will only be applicable in the applied space you are in (regarding your galaxy - leave the milky way , and mathematic algorithms will have to be changed - 5+5= 20.)

-----

The Human brain cannot possible comprehend infinity. It can comprehend constraints on infinity. 1+1=2 , you constrained infinity to fit into an understanding you can perceive.

So i guess the professor is right. Infinity is the expression of God.

--------

0 is a "place holder / number" meaning there is a non-existent numerical order in an expression in which the number is used (0).

--------

You ask how God is expressed in infinity? Because infinity is infinite only through the basis of progression. Meaning infinite cannot be infinite without an expression existing first. Some how , some way , an expression was created to begin infinity.

This is where all your "weird" science comes into play.

Here is the expression of what i am saying to you -

1-1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 111111111111111111111111111111111111111111111111111111111111111111

Creation is literally shown from current understanding to be expressed in the number one. Some how an action occurred for a problem to come into existence.

Simply apply newtons law , that it takes an action to create a reaction.

Originally posted by OutKast Searcher

Originally posted by ClydeFrog42

You see, the idea of this process is represented by limits. As this continues on, as we *approach* infinity (as our number gets larger in larger), the answer approaches zero.

reply to post by WhatAreThey

 

You are making the false assumption that infinity is something that can be "approached". As if you keep dividing forever you will hit infinity and zero at the same time....

This is fundamentally flawed logic. You can divide as long as you want, you will never reach zero, nor will you ever (even if you divide the number 1 in half using a supercomputer for the rest of time) reach infinity.

Maybe its convenient to believe that you can "approach" infinity, but infinity is unapproachable. It is a concept used to describe something that has no limits... so it makes no sense to use infinity to describe limits...

Literally senseless. You are treating infinity as if it is a certain value that can be attained. It is not.

No, he is absolutely right in his description of the limit function.

And you can "approach" infinity...but you can never reach it.

For 1/x as x approaches infinity, the answer approaches zero. X will never reach infinity, and the answer will never be zero. This is the whole point of the limit function...to find the limit.

Instead of talking about arbitrary 'limit functions', i think it would be much more fun to talk about "reality".

If we should talk "True Reality", then the answer would be of course, that we cannot "approach" infinity.

It is only through true reality that we'll ever be able to fully understand and comprehend the concept of infinity, so maybe it would be better to combine the 2 forthwith, me think - perhaps!