pUrNamadah pUrNamidam ..........Infinity and zero

[Guest guest]

Namaste Vishalji,

 

Your post drew a kind attention to my post on the mathematical

interpretations of infinity. Unfortunately, I beleive I should never

have posted it, since I am already seeing some small

misinterpretations. Shall I take one more opportunity to try to

explain this? Please donot misunderstand me. I have great

appreaciation for the fact that you atleast read the message and got

most of it.

> Infinity is equivalent to 0 .

 

This is not a mathematical principle. Atleast not till now. And even

from the standpoint of philosophy, it cannot be true. It is known that

 

0 + 0 = 0

0 - 0 = 0

0 * 0 = 0

0 / 0 is an undefined operation, but in the limit when the numerator

and the denominator only tend to zero, they may be equal to one or

the like. For example the limit sin(x)/x in the limit x tends to zero

is 1, but 0/0 itself is not uniquely expressible in mathematical terms

 

On the contrary, while

 

infinity + infinity = infinity

infinity - infinity = infinity

infinity * infinity = infinity

infinity / infinity = 1 definitely

There is no need for the limit in the last operation. This means that

infinity itself is indivisible further into more parts. If we take

quantities that tend to infinity in the numerator and the

denominator, on the contrary, we cannot predict the result in

general.

 

For example, r^2/r is one such example, where r is a very large real

number. Both the numerator and the denominator are not equal to

infinity, but tend to it. But in the limit r^2/r is infinity.

 

Now on the contrary, r/r^2 also has numerator and denominator not

equal to but tending to infinity, since r is a very large real

number. But in the limit, r/r^2 tends to zero!

 

Hence the limit concept is to be applied with great care in this

situation. The case of division of infinity itself by infinity, is

different. The numerator and denominator are both infinity. The

result is based on the fact that there can be no other infinity. If

there exists, then neither the first nor the second inifinties would

truly be infinite, since there is something not contained in each of

them, which is the other infinity.

 

But most of all, there is a very great distinction between zero and

infinity.

 

0 + anything else = anything else

infinity + anything else = infinity

 

This is equally important while understanding pUrNasya

pUrNamAdaya.....

 

I would however, engourage you to go ahead and try to prove it if you

really feel so and write a paper about it to let the mathematical

world know of it.

> If Infinity is divided, multipied, added or substracted. Result

will always be infinity.

 

Please note my message carefully. The last question in that message

discusses division of infinity by infinity.

> If O (nothingness) is divided, multipied, added or substracted.

Result will always be 0.

>

 

The case of division of 0 by 0 has been discussed here in the

beginning. So is the case of any other number divided by 0.

> If there are infinite elements between 0 and 1 then each element

should be equal to 0.

 

I think you have misunderstood this. I did not mean this. Each

element in the interval 0 to 1 exists and is not reduced to

nothingness. But the number of elements in the interval 0 to 1 equals

that of the entire set of real numbers. The concept of countability

of sets is important here. Two uncountable sets can be compared only

by a one-one-correspondence. I shall explain this if the readers

don't understand this. But I think this is a fairly famous result

shown by Georg Cantor who unfortunately, due to inability to face

criticism (due to his obvious pitiable spiritual ignorance) lost his

mental balance and spent the rest of his lifetime in mental

hospitals.

> Infinity and 0 can be understood only in limit. Hence both are

equivalnet.

>

 

Infinity is best understood in the limit, for it cannot be understood

otherwise by the intellect. It is however the Self, the bodha, the

jnah. But it is complete in itself. Zero need not be understood in

the limit, although it may be, for your own purposes.

 

The idea that infinity and zero may be the same, reminds me of the

way I was misinterpreted in the 'Buddhism is the same as Advaita'

post, where some learned members were telling me the difference

between pUrNa and shoonya. I agreed with them, but possibly they did

not recognize that agreement.

 

According to the most traditional form of Buddhism - Theravada,

shunyata is not the absolute Truth. The Arahant (Enlightened one) is

complete (paripunna - the Sanskrit word paripUrNa), and has realized

the absolute truth. The nature of the absolute truth was however

never discussed in the Pali Canon or by the Buddha for the reason

that it was to be realized, not discussed. The Mahayana on the

contrary thinks that shunyata represents the absolute Truth. This is

not in conformance with the Pali Canon. They apparently mistook

shunyata to be the absolute Truth. Hence Shankara refuted many

schools of Buddhism, excluding Theravada, which was no longer in

India.

 

The concept of shunyata in Theravada and hence in the Buddha's

teachings was that all transients in the universe are impermanent and

hence non-existent (The 'non-existent' sense here is to be understood

as 'impermanently existent') Hence our incorrect cognition that we

posess something is shunya in reality (in other words, has no essence

or ground at all or is just ignorance) This concept was extended in

the Mahayana sect to think that everything is shunya and hence

shunyata as the absolute truth. Nevertheless, realizing that every

thing in this universe is impermanent is an important part of the

Buddha's teachings.

 

Anyway, let's not digress. I made clarifications just so that no more

misinterpretations of my posts may take place. I grabbed this chance,

to let members, especially Sri Ranjeet and Sri Chittaranjan, know

that I agreed to their point that the Absolute cannot be shunya. I

hope to get another chance to clear off misinterpretations of my

posts on the 'Why a commentary? Swimming Analogy' issue.

 

Satyameva Jayate Naanrtam

[Guest guest]

Namaste Shri Balaji,

 

advaitin, "Balaji Ramasubramanian"

<balajiramasubramanian> wrote:

> I grabbed this chance, to let members, especially Sri Ranjeet

> and Sri Chittaranjan, know that I agreed to their point that

> the Absolute cannot be shunya. I hope to get another chance

> to clear off misinterpretations of my posts on the 'Why a

> commentary? Swimming Analogy' issue.

 

 

Thank you Shri Balaji for the clarification. Shri Ranjeetji may not

be able to read it as he is not a member of this list anymore.

 

Regards,

Chittaranjan

[Guest guest]

Namaste all,

> Thank you Shri Balaji for the clarification. Shri Ranjeetji may not

> be able to read it as he is not a member of this list anymore.

>

 

It is most unfortunate for him to leave the list. I feel extremely

sorry for this. I understand that I stand responsible for this. If

the group feels that an appropriate action is to be taken against me,

kindly do so.

 

I requested to Sri Ranjeetji in post 21954 to stay. I am sorry for

the consequences. If something could be done, please do let me know.

Should I write to him personally? Is he really cross with me? Maybe

he would just delete my email.

 

-Balaji

[Guest guest]

Namaste:

 

Mathematics of numbers is a fasinating field. The algebra of numbers

is well defined and how deal with 'zero' and 'infinity' are

available in standard mathematical texts. I recommend the book with

the title, "One Two Three . . . Infinity : Facts and Speculations of

Science" by George Gamow (Author) to members who want to pursue

further. This book is available in most of the public libraries and

is available in the Internet book stores such as amazon.com.

 

Sri Nair and Sri Sunder had a question regarding the multiplication

of zero and infinity and here are my understanding:

 

The following are undefinable according to text books on mathematics:

(1) (zero/zero)

(2) (infinity/infinity)

(3) (zero*infinity)

 

Warmest regards,

 

Ram Chandran

[Guest guest]

Namaste Shri Balaji,

 

advaitin, "Balaji Ramasubramanian"

<balajiramasubramanian> wrote:

> Namaste all,

>

> It is most unfortunate for him (Shri Ranjeetji) to leave the

> list. I feel extremely sorry for this. I understand that I

> stand responsible for this. If the group feels that an

> appropriate action is to be taken against me, kindly do so.

 

 

I don't think you should consider yourself responsible for

Ranjeetji's actions. Everybody is responsible for his or her own

actions. But yes, it is unfortunate that he left - I for one will

miss his words of wisdom. I was immensely impressed by his article on

dharma.

 

Regards,

Chittaranjan

[Guest guest]

Namaste Balaji

 

You are right and have proved mathematically that infinity cannot be zero.

I agree.

 

But this applies only to the infinities and zeros which are not absolute.

I was talking from the absolute standpoint (paramarthik). I should have made

this clear in my previous mail.

Anyway i appreciate your efforts for clarification.

 

Let me clarify.

Take for example -if we count stars in night sky, 1 star..2 star....infinite

number of stars.

This infinite number of stars is not absoulte infinity. We can have infinite

real numbers, infinite dust particles, infinite atoms, infinite electros

etc..ect...

 

Now example for zero - i have a pot in front of me. If that pot is removed away,

there will be no pot there. Means 1 pot - 1 pot = 0 pot. Now 0 pot or this

nothingness of pot is not the absolute nothingness. I can say i have 0 car (i

dont have a car), i have 0 bunglows !!!!

 

Absolute infinity is sat or existence.

existenec of what ? just existence. If not then it will be called asat.

 

Absolute zero is asat or non-existence.

non-existence of what ? just non-existence. If not then it will be called sat.

 

how will you differentiate sat and asat (existence and non-existence) ?

There is absolutely no way to do that. Because they are in essence same.

They are counterparts of each other. There can be either sat or asat. Never

both.

 

You have to choose any one of them and build your siddhanta.

If you choose sat (infinity) you will end up developing advaita .

If you choose asat (zero) you will end up developing the shunyavada.

 

pUrNa can be either infinity or zero, according to how you see. This happens

because we try to express that thing which is un-expressible (anirvachaniya). In

that process we end up giving some names and meanings to that un-expresible

thing. This process of assigning names and meanings leads to different concepts

of the same un-expressible thing. We have to comprehend that, it will surely

help us to become that.

 

pUrNa is Zero, pUrNa is infinity, pUrNa is Brahma.

 

hope i have made myself amply clear.

I agree with you, there is no point in digressing as each one (great acharyas)

are correct from their respective standpoint.

ekam sadvipra bahuda vadanti.

 

Om tat-sat

Vishal

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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[Guest guest]

Namaste Sri Ramji,

 

I respect your profound understanding of mathematics and I also learn

that you must be a professor of mathematics. However, there might be

a small adjustment in terms used to be made.

> The following are undefinable according to text books on

mathematics:

> (1) (zero/zero)

> (2) (infinity/infinity)

> (3) (zero*infinity)

>

 

While surely the first and the last are undefined, as I have pointed

in my first discussion of the mathematical interpretations, the

second is not undefined.

 

The limiting expressions like x/y where x and y are both TENDING to

infinity (not equal to infinity) may not be defined always. Sometimes

we may get a non-defined result and sometimes a well defined one. But

when infinity itself is divided (partitioned) into infinity, it

leaves unity. Just shows that there cannot be two distinct

infinities. If there were, then they won't be infinite. A deep

advaitic concept!

 

Now, we may say that the same arguement is true of zero - that there

exists only one unique zero. But then, zero is divisible, the result

is zero, unless we divide it by zero itself. But the fact that

infinity / infinity = 1 does not mean that infinity is divisible by

all. Infinity is non-divisible. The term non-divisible is different

from indivisible. Again an advaitic concept!

 

Besides, zero contains nothing. Infinity contains everything,

including zero. Therefore, while zero/zero is undefined, infinity by

infinity is definitely 1.

 

In fact I had a paper on this, when I was just in school - class XII.

It was even sent to the IMU, but it faced lots of criticism. Some

people were also however, supportive of my ideas, like Prof. Muharem

Avdispahic from Sarajevo and Prof. T A Gillespie of the Edinburg

Mathematical Society.

 

But unfortunately, these things don't matter for admissions in India.

I applied to BITS Pilani and there they wanted a person with 100% in

four subjects! At IIT, I only got a 750 rank or so. Could not fetch

me my branch of interest. So I joined NSIT, University of Delhi.

 

It then matured when I came to college, when I came in contact with

Prof. Vijay Gupta, teching at NSIT (my college). Currently there is

lot more work going on in it. Before, I can present the idea, it

should be found useful. Unfortunately the IMU is not ready to

recognize the importance of the fact, and is concerned only with its

applications. Unfortunately, that paper cannot be disclosed in non-

international councils. If I do so, the paper would be immediately

disqualified from open literature publications. The results however,

in abstract form as I have presented here can be open.

 

Well, I am not a mathematician here! I am by profession an

electronics engineer and love my field of engineering too. But I

still have a great interest in mathematics.

 

Please don't misunderstand me. Your ideas on infinity are not wrong,

and shall be accepted until the world wakes up to this new idea.

Nevertheless, you have not incorrectly represented mathematics. I

beleive, your understanding of mathematics borne out of experience of

so many years is surely more profound than mine.

 

Satyameva Jayate Naanrtam

[Guest guest]

Namaste Vishalji,

 

I am impressed with your points. I must agree with you. But just one

small note. Normally, the number of particles in a pot are said to be

non-finite, not infinite. There is a trace difference, usually

neglected in practice. But such disticntion is required for one to

understand a paper on just inifinity. Otherwise, I beleive whatever

you have said was correct (in my opinion).

 

I think we have one who has beautfully understood whatever I pointed

out. If you are a mathematician, will you kindly honor me by your

presence in a mathematical conference, where I propose to present my

paper on infinity?

 

-Balaji

[Guest guest]

Namaste Sri Balaji:

 

I do believe that you have strong background in mathematics but I

may have to disagree with your contention that (infinity/infinity)=1.

 

Interestingly, this question was discussed in mathematics forum at

the following URL:

http://mathforum.org/library/drmath/view/53337.html

 

Let me also pointout that mathforum is a reputed organization

dedicated to answering the questions raised by students in the US

highschools. The answers they provide are quite authentic.

 

4/10/96 at 18:50:50

"Jeremy Vigneault"

Infinity question

 

Dear Dr. Math,

 

I have a question maybe you can answer. My electronics teacher

and I are having a disagreement. He says that Infinity divided by

Infinity equals one. I most certainly disagree; I say that

infinity over infinity is indeterminate, because infinity is a

concept, not a finite number. Could you please help me in this

discrepancy?

 

===============================

4/12/96 at 21:36:13

Doctor Syd

Re: Infinity question

 

Dear Jeremy,

 

Good work! You are correct. Many people are confused by

infinity; you are right that is a concept and not a number the way

that 28 is a number. There are sort of some different "sizes" of

infinities, so this means that a quotient that looks like infinity

over infinity can sometimes be a real number, and sometimes it is

just infinity.

 

Warmest regard

 

Ram Chandran

 

Note: I recommend the following links for maths lovers.

http://mathforum.org/dr.math/faq/#others

[Guest guest]

Namaste Sri Ramji,

 

While I did go ahead and represent things in the algebraic for

infinity / infinity = 1, what I have to also mention is that the

division we are talking of here is not the algebraic notion of

dividing one quantity by another. Such an operation is valid only for

quantities and not concepts as you point out. Surely from the

algebraic sense, infinity/infinity would be undefined. But

unfortunately, infinity does not fall under the jurisdiction of

algebra for us to consider its definition. So its being undefined in

algebraic terms means only that it cannot be represented as any

quantity.

 

The way it is to be really represented is 'infinity when divided into

infinity results in unity'. This statement itself is a concept and

not an algebraic expression. You have correctly pinched me on my

nerve, when I represented it algebraically! This was a very important

point for you to have highlighted to everyone here.

 

Btw, you seem to be a great professor of mathematics, when I have

enough time and money, (I mean I hope I would have) sometime in

August or September this year, I might go for a conference in

Stockholm to present this concept. Could you kindly honor me by your

presence.

 

Shri Gurubhyo Namah, Harih Om

-Balaji

[Guest guest]

Namaste Balaji

 

It is interesting to know that you will be presenting a paper on mathematics.

 

By the way i am not a mathematician but surely interested in maths as it is a

tool to reveal the reality. Almost like shabda pramana.

 

Wishing you all the best.

 

Om tat-sat

Vishal

 

 

 

 

 

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