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## #1001 2012-06-24 22:46:29

bob bundy
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### Re: 0.9999....(recurring) = 1?

Yes I did.  You have said your prof says it doesn't exist.

Either you misunderstood; or he was trying to provoke critical thinking (succeeded too); or his statement is easy to disprove.

You do this by writing 0.99999 recurring on a piece of paper and say "Look! There it is.  I see, therefore it is."

It has as much right to be considered to exist as 'pi', or 'e' or ∞

What is of greater interest surely, is,  how does this number behave?  And all the evidence suggests it behaves just like 1.

Mathematics isn't 'the real world'; it attempts to model the real world.  And to do this we have to make up idealised concepts.  Here's a list of a few:

points with zero dimensions
infinite planes
frictonless pulleys
angles that can be measured with perfect accuracy (have you ever tried to draw a triangle, measure its angles and check what they add up to?)
decimals with an infinite number of digits
hyperspace
the multiverse

Do any of these 'exist'?

Bob

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

## #1002 2012-06-24 23:01:48

Stangerzv
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### Re: 0.9999....(recurring) = 1?

You can perceive 3 because it is part of decimal system. Human developed numbers according to our fingers. How many fingers do you have? 10...so what is 3? ..one two three fingers..can you calculate 1/2? yes..0.5 or half fingers..can you quantify 1/3..no way..until forever 3333333 would go on. There is no absolute value you can quantify from 1/3 using our finger system or decimal! Infinity is a concept but numbers is real..if you play with infinity then you compromise many things. Therefore, anything deals with the infinity like irrational numbers decimal places..you can never actually write it down, the fraction we representing them is more like a symbol not a value. I can prove you that 0.999999999.. can never be 1 because (1-0.99999999999..)x infinity not equal to zero. Yet (1-1) x infinity=0! Can you give me three apples? Yes you can but can you give me exactly

apples? I hope you could:)

I think we human didn't invent numbers because it is already there even before we existed. We discovered mathematics and we don't invent anything dealing with mathematics. For example, Pythagoras didn't invent his theorem but he discovered it. This is because the movement our our galaxy, sun, earth, planets etc  involved Pythagoras mathematics long before we existed on this planet.

Basically x^0=1 because
and
Mathematics is a knowledge field that depend on proof because if anything could contradict it, would prove it wrong. Pythagoras believed that numbers were not only the way to truth, but truth itself. http://www.ancient.eu.com/article/213/ . While a concept not always true, could be wrong sometimes!

Last edited by Stangerzv (2012-06-24 23:04:10)

## #1003 2012-06-25 00:29:31

bob bundy
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### Re: 0.9999....(recurring) = 1?

hi Stangerzv

Thanks for the link.  Beware of trusting in a single resource.  Pythagoras was not the world's first mathematician.

Here's a selection of reading for you to back up my assertions.

Hope you find some of them enlightening.

http://en.wikipedia.org/wiki/Pythagoras

http://aleph0.clarku.edu/~djoyce/mathhi … ology.html

http://www.whodiscoveredit.com/who-disc … eorem.html

http://www.wolframalpha.com/input/?i=0.9+recurring

http://openlearn.open.ac.uk/mod/ouconte … ection=1.2

Bob

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

## #1004 2012-06-25 10:47:28

Stangerzv
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### Re: 0.9999....(recurring) = 1?

*Pythagoras was not the world's first mathematician.  * I didn't say he was the first mathematicians but I gave his name as example. Mathematics was there even before human were first on earth. This universe is governed by mathematics billions years ago, I think the first concept of singularity ever known to us is the creation of this universe, when t=0, the volume of universe is zero but with infinite density. If you read the Hindus manuscripts you would find that they had done earlier many of the mathematics found in Europe or Middle East. Yet Hindus civilization not even older than the Sumerian in Iraq, Sumerians had Pythagorean triple ages ago written on stone tablet. Where ever you found wheel or circle, then you can find pi and Pythagoras theorem. Now they found a new civilization in Turkey dated back 12,000 years and they predated the invention of wheels. http://www.youtube.com/watch?v=TZ0ViMVxKZA&feature=related

Last edited by Stangerzv (2012-06-25 11:13:16)

## #1005 2012-06-25 11:02:40

anonimnystefy
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### Re: 0.9999....(recurring) = 1?

Yes that is true. Numbers, as a concept, existed since always. But it doesn't change the fact that the imaginary unit, i, is not as real as the number 3. Actually, they are neither real (in the sense that they don't exist). There are only there representations, wheter they are apples or graphic representations i.e. digits.

But why in the world do you think that the universe had infinite mass at the point of time t=0 ?

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #1006 2012-06-25 11:11:43

Stangerzv
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### Re: 0.9999....(recurring) = 1?

Sorry anonimnystefy..not mass but density. Like the birth of supernova, in the beginning of its creation, the mass of 1 miligram of it could be several times or perhaps million times more dense than our entire solar system masses combined together. I think imaginary numbers are like the images in the mirror, they look real but just images and they need real things to exist.

## #1007 2012-06-25 11:17:27

anonimnystefy
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### Re: 0.9999....(recurring) = 1?

That's okay then. I don't know how much astrophysicists would agree with you, but we are doing math here.

I repeat once again what Bob and I have already said. No number is real (in the non-mathematical sense).

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #1008 2012-06-25 11:50:17

Stangerzv
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### Re: 0.9999....(recurring) = 1?

To be honest we are not real too:) Nothing is real actually in this world, our intelligence is about comparing things, the unit of Energy Joule is not exactly a unit of energy in real sense but representation of comparison what this guy name could do to a temperature etc. Even a meter length is not real but a comparison of a metal bar stored somewhere in France. Numbers act the same ways too. They are there for us to compare but there are numbers we can't compared like irrational, imaginary and infinity numbers. Basically, astrophysics got to do with mathematics, like singularity 1/0, it doesn't exist in our limited knowledge yet it does exist in the formation of this universe or black holes for examples. The 0.99999999.... is the same thing as playing with singularity, to get 0.99999..you need to do this 1/(1000000..recurring zeros until infinity and at the end of infinity you need to finish it with digit 1). Maybe all numbers are real, even the irrational, imaginary,infinity etc but our brain capacity couldn't cope with it. Like we could have a perfect circle yet pi is irrational. We could draw a perfect square with a unit sides yet we failed to measure its diagonal with 100% accuracy. We can see it yet we can't measure accurately 100%, it is sad somehow:). There is limitation in us to understand all mathematics but if there is the One who invented mathematics that we found in this universe He must be endless genius and He is either infinite or more than it.

## #1009 2012-06-25 12:19:05

anonimnystefy
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### Re: 0.9999....(recurring) = 1?

First, I must say that you are definitely right about on thing and that's that no unit of measure is real in the everyday sense of the word. You can have a 220 volts light bulb, but you cannot 220 volts. Most discussion about realness of a measure is that of a second. Time is something that causes much debate.

Now you are getting carried away. In mathematics, you have an exact definition for everything included in it (except for elementary objects such as the set and the point). Square root of two and pi are real numbers,but infinity and i are not. i is an imaginary number and infinity is a hypereal (and a surreal, I think). You cannot go around proposing that all numbers are real. Mathematicians will laugh at you and throw octonion and sedenion multiplication tables at you.

What I will ask you to do is keep God out of this. Maybe there were all sorts of mathematics out there, but the humans "stumbled upon" theone we know today because they have defined it. That definitely doesn't mean that they do not understand it. Here is a little analogy. Words have also, by the same logic, been around before humans. Does that give us the right to claim that we cannot understand words? Of course not! That, of course, doesn't mean that there is somebody who knows all the words (or all mathematical concepts), but every word/concept that exists (meaning that humans have defined it) is definitely understood by somebody.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #1010 2012-06-25 15:13:32

Stangerzv
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### Re: 0.9999....(recurring) = 1?

Of course you are right! I didn't mean all numbers are real of course there are imaginary numbers etc. But in sense of human capability of understanding it, even when it is real number it doesn't looks real to our understanding like the value of pi, we can have exact circle yet the pi in it is irrational, it is a mystery. I just pointing that, that even the so call  imaginary numbers does exist in many real things or coexist with real numbers like roots of equation. Not people like Ramanujan formulated 1+2+3+4...=-1/12 got carried away? Maths were based on thinking and opinions of people and there are some maths which were considered fringe science and later on were proven to be true. Words or languages evolved through times and we human made them, English didn't exist 50,000 thousands years ago, same with the word GOOGLE, this word wasn't there before us. Unless you do believe that human was from Adam and Eve and they already made with language embedded in them. Mathematics is the only thing that you can make all people to agree 100% that something is true or not, our opinions differ but not the mathematics. Pythagoras Theorem doesn't need our opinion to be true, itself is true, we give opinions and the true opinion will fill in the gap eventually. This is why you can give your opinions what ever you like because restricting opinions would make Mathematics static. From garbage opinions there could be something true.

Basically, I don't think I am too much to say if there is the One who invented the mathematics the one must be super genius etc. Because not the same thing applies in the quest of God particle or Higg Boson? They had built multi billions facility to find this mystery thing which is is thought to be the most fundamental subatomic particles which could be the fundamental building block of this universe. http://www.guardian.co.uk/science/2011/nov/07/massive-hunt-god-particle-ian-sample-review . They built 7.5 billions Euros Hydra Collider to find God Particle, shouldn't they keep the word God out of this too? Perhaps Euler, one of the greatest mathematicians shouldn't even ventured further to proof the existence of God http://en.wikipedia.org/wiki/Leonhard_Euler#cite_note-41 because is it not ethical to link anything to one's belief? Our knowledge evolved from people opinions regardless what they are believing in and I stand on this.

## #1011 2012-06-25 17:07:43

bobbym
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### Re: 0.9999....(recurring) = 1?

Hi Stangerzv;

You like the integers, luckily there is a whole branch of math for that. It is called Number theory. You can stay in it all your whole life and never have to see a decimal point.

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #1012 2012-06-25 18:05:24

Stangerzv
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### Re: 0.9999....(recurring) = 1?

Hi Bobbym!

I like all numbers:). I am currently working of sums of power for non-integers. There is a lot of things making us confused when dealing with infinity. Here is my Riemman's Zeta Function derived using my sums of power formulation.

By letting s=2, this equation would give you 4 not (pi^2)/6.

As for integers I am done with them, I had formulated enough formulation for them on my capability. Now I am working on non-integers but not like whole numbers, what you get from non-integers is approximation. I have developed numerical analysis for non-integers power like how to add this equation
, the method not that amazing because sometimes it takes you to infinity to calculate a simple value.

Last edited by Stangerzv (2012-06-25 18:06:55)

## #1013 2012-06-25 21:43:20

anonimnystefy
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### Re: 0.9999....(recurring) = 1?

I have a question for zeta function summation.

1) How did you derive the sum and limit on the far right?

2) How did you evaluate that to 2?

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #1014 2012-06-25 22:51:12

anonimnystefy
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### Re: 0.9999....(recurring) = 1?

#### Stangerzv wrote:

Of course you are right! I didn't mean all numbers are real of course there are imaginary numbers etc. But in sense of human capability of understanding it, even when it is real number it doesn't looks real to our understanding like the value of pi, we can have exact circle yet the pi in it is irrational, it is a mystery. I just pointing that, that even the so call  imaginary numbers does exist in many real things or coexist with real numbers like roots of equation. Not people like Ramanujan formulated 1+2+3+4...=-1/12 got carried away? Maths were based on thinking and opinions of people and there are some maths which were considered fringe science and later on were proven to be true. Words or languages evolved through times and we human made them, English didn't exist 50,000 thousands years ago, same with the word GOOGLE, this word wasn't there before us. Unless you do believe that human was from Adam and Eve and they already made with language embedded in them. Mathematics is the only thing that you can make all people to agree 100% that something is true or not, our opinions differ but not the mathematics. Pythagoras Theorem doesn't need our opinion to be true, itself is true, we give opinions and the true opinion will fill in the gap eventually. This is why you can give your opinions what ever you like because restricting opinions would make Mathematics static. From garbage opinions there could be something true.

Basically, I don't think I am too much to say if there is the One who invented the mathematics the one must be super genius etc. Because not the same thing applies in the quest of God particle or Higg Boson? They had built multi billions facility to find this mystery thing which is is thought to be the most fundamental subatomic particles which could be the fundamental building block of this universe. http://www.guardian.co.uk/science/2011/nov/07/massive-hunt-god-particle-ian-sample-review . They built 7.5 billions Euros Hydra Collider to find God Particle, shouldn't they keep the word God out of this too? Perhaps Euler, one of the greatest mathematicians shouldn't even ventured further to proof the existence of God http://en.wikipedia.org/wiki/Leonhard_Euler#cite_note-41 because is it not ethical to link anything to one's belief? Our knowledge evolved from people opinions regardless what they are believing in and I stand on this.

Now you are contradicting yourself. If all mathematical concepts were created by some supreme being before the humans, then shouldn't the same be true for words.

But I don't think they were created by anyone or anybody. They just were and are and will be.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #1015 2012-06-27 19:48:16

TESTU
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### Re: 0.9999....(recurring) = 1?

This Sounds like a Real Problem!

But!...0.9999....(recurring) is like the Math Universe! for 0.9999....(recurring) to Equal 1

Would be the same as Gathering All the Stars in the Universe ?? and then putting them in a Box and Calling the Box 1

## #1016 2012-06-27 21:21:08

bob bundy
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### Re: 0.9999....(recurring) = 1?

hi TESTU

Would be the same as Gathering All the Stars in the Universe ?? and then putting them in a Box and Calling the Box 1

Mmmmm.  But there are only a finite number of stars.  And you could just as easily call the box 'fred'

If you want an analogy how about this one.

A frog starts hopping at point A.  His first hop is 1 metre.  His second is 1/2 metre.  His third is 1/4 metre.  And so on, each hop half the size of the one before.

He is aiming to reach point B which is 2 metres from A.  Does he get there?

Bob

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You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

## #1017 2012-06-27 22:13:27

anonimnystefy
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### Re: 0.9999....(recurring) = 1?

Can I answer this one? Can I?

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #1018 2012-06-27 22:32:55

TESTU
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### Re: 0.9999....(recurring) = 1?

Have to Correct You Bob! There can only be a finite number of stars!... If the Whole Universe has been Mapped!?

Which won't Happen in Your life time or Mine!

This should Help any Doubters!...And is a Very Good example Why Estimated Math is BAD Math!

And the Reason Why Infinite/Recurring 0.999... = 1 ? Is Estimated Math!

http://blogs.discovermagazine.com/80beats/2010/12/01/the-estimated-number-of-stars-in-the-universe-just-tripled/

Last edited by TESTU (2012-06-28 00:51:26)

## #1019 2012-06-27 22:52:18

anonimnystefy
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### Re: 0.9999....(recurring) = 1?

Hi TESTU

If you think that we cannot know how many stars there are because we cannot yet discover them all, you are incorrect. Astro-physicists have estimated the number of particles in the universe to a finite value, so there must be only a finite number of stars.

But the star argument doesn't apply to the 0.999...=1 discussion, as Bob pointed out.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #1020 2012-06-27 23:46:34

bobbym
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### Re: 0.9999....(recurring) = 1?

Hi TESTU;

Sorry, to interrupt these talks but don't you have a problem in the other thread concerning lotto that need clarification? Or do you no longer need the answer?

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #1021 2012-06-28 18:13:41

TESTU
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### Re: 0.9999....(recurring) = 1?

Quote: "A frog starts hopping at point A.  His first hop is 1 metre.  His second is 1/2 metre.  His third is 1/4 metre.  And so on, each hop half the size of the one before.

He is aiming to reach point B which is 2 metres from A.  Does he get there?

Reply...Not if it get's Run over by a Car Etc.

## #1022 2012-06-28 18:35:24

Stangerzv
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### Re: 0.9999....(recurring) = 1?

Hi anonimnystefy

The derivation is quite lengthy:

By using my formulation for sums of power for integers and non-integers power, you would get this relationship,

Setting p=-s

Taking limit n to infinity and simplifying the coefficients yields,

Further simplifying you get the equation above. Take note that when p is non-integers, the coefficients of sums of power become unbounded.

Last edited by Stangerzv (2012-06-28 18:51:02)

## #1023 2012-06-28 19:11:56

Stangerzv
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### Re: 0.9999....(recurring) = 1?

Hi Testu

Basically nobody knows whether this universe is finite or infinite but many thinks it is infinite as the universe still expanding and the birth or stars still occurring. If you look into the formation of this universe, in the beginning, the volume of this universe is zero with infinite density (singularity). From zero to something after t=0, since the density is infinite, the formation of mass of particles should be also infinite. http://en.wikipedia.org/wiki/Gravitational_singularity . In other words, all the things or masses in this entire universe could be confined into a single piece of thing which has the volume near zero after t=0s. If this is a singularity, then the universe is infinite or maybe so big that we couldn't simply comprehend because there is a place in this universe where the space expanded further away way before a light could reach it. How big this universe is, perhaps as big as 1/0 (division by zero).

## #1024 2012-06-28 21:35:11

TESTU
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### Re: 0.9999....(recurring) = 1?

Hi Stangerzv 1/0 = 1 Because No Value has been Divided into the Start Value of 1

I am sure the Universe is Bigger than 1 ... But 1 what! ? 1 x the Largest Space we Can Calculate! But then we are Back to  Estimated Math!

## #1025 2012-06-28 23:13:02

bobbym
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### Re: 0.9999....(recurring) = 1?

Hi;

1 / 0 is not 1. It is undefined to divide by 0.

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

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