The Mysteries Of The Numbers "Zero" And "Infinity"

Yes, its very interesting.

you can refer to book of " math idea" writed by Clin. there are lots of examples of such things.

Having been out of college for quite some time, when you brought this up, reminds me of courses I took in complex and invisible numbers.

You sparked my interest, I will have pull my text books out and brush up.

thanks,

Hi. Phoenix... I have finished university 16 years ago... This doesn't mean anything...

I thought all these recently... And I wanted to share this thoughts...

Oh no, actually, I have finished university 18 years ago (I forgot the 2 years of the military service)... Oh God, it's so long time ago...

somehow i think there is some misintrepretation of limits that you are eluding to. Some people who understand the math get lazy and drop the limits term over time, and others who don't understand it well misunderstand this to mean a direct solution. n/0 never equals infinite, it just approaches infinite. n over infinite doesn't equal 0 it approaches 0, but is always larger or smaller than 0.

I didn't elude (or misunderstand) limits... And that's why I began the presentation of my thoughts with lim_x→0(n/x)=∞ ... I believe that the correct way to get a solution is the limits... Of course, this makes sense and gives correct answers... But, beyond limits, I dared to manipulate the "absolute concept of 0 and ∞"... In the expression "n/x" when x tends to be zero then n/x tends to be infinity... But the expression "n/0" (which means that the denominator is exactly 0) has "no meaning"...

So, I agree with you...

Hi George,

In your earlier thread concerning "Black holes, an issue for discussion", I said here that lim _{x -> n} 1 / (x - n) = ∞ = singularity.

I was simply trying to point out that certain limits reach a point where they seem to break down, i.e., 1 / 0, etc. I realize that in the limit I posed, you never actually get to zero, but at what point do you conclude that carrying the limit to its ultimate conclusion has no meaning. Same with a singularity.

Somewhere within the depths of that black hole, we reach the point where x = n, no?

-John

Hi, John... That's a good point... (although I admit that, in a first view, I couldn't understand what you were trying to say...)

In a way, you could say that it's a similar situation... As you go inside a Black Hole, you approach the singularity by the means of the General Relativity... But at the singularity (or, maybe, at the area very close to singularity) the General Relativity breaks down and the singularity itself seems that has "no meaning" at all...

But, as Jorrie said, maybe near the singularity the Quantum Gravity plays the dominant role (as the General Relativity is unable to give a reasonable explanation to that situation)... And Quantum Gravity is still under research...

I wonder if everyone of your western students has to serve in the army for two years during your university study?

in other words, has everyone studnet ever took part in the army?

In our country, college students neednt to serve in army. but now the situation is changing. it seems we begine to learn your system. and the student can take part in army and then continue his education in university.

"I wonder if everyone of your western students has to serve in the army for two years during your university study?"

No during the university studies but after the university studies... Unfortunately, in Greece the military service is obligatory... In other western countries is voluntary... Nowadays, in Greece the military service is reduced and it's 1 year...

The Isha Upanishad of the Yajurveda (c. 4th to 3rd century BC) states that "if you remove a part from infinity or add a part to infinity, still what remains is infinity".

joshua

G.K.

Good post. I'm still working through the math, but you raise excellent points about our use of ∞

Thanks,

Tom

hmm ?

n/0= ¥ if n=0.¥ so n=0? or( n/¥ =0)

if ¥/ ¥ =1(unity factor suppose) than 0/0=1 how?

if ¥/¥ =n than 0/0 =n how?

so , 0<n<¥

Hi Vikas... (when you copy-paste from a word file the ¥ appears instead of ∞ ... don't forget to correct it...)

I'm not sure that I get what you are trying to say... (don't hesitate to use more words in order to be comprehensible...)... So clarify this, pls...

I had some arguments in order to show that (if n is any finite number) n/0≠∞ ... The expression "n/0" simply has no meaning at all...

"if ∞/∞ =n than 0/0 =n how?"

Of course these are both true as ∞.n=∞ & 0.n=0...

As you see, although the "n/0" has no meaning, the "0/0" has meaning and its result is indefinite...

(So "n/0" has no meaning if "n" is any finite number...)

[ But what about "∞/0" ???... ... is this meaningful???...

"∞/0" can't be any finite number or 0 (as any finite number or 0 multiplied by 0 gives 0 and not ∞ )... But can it be infinite???... If ∞/0=∞ then 0.∞=∞... do this makes sense???... Hmmm... ... there's a lot of discussions about the product 0 & ∞... Some claim that it is undefined (or it's indefinite)... maybe it has to do with the issue of «how fast do you approach the "0" or the "∞"» that can give you any possible result (from 0 to ∞)... well, with this point of view the "∞/0" is, also, undefined (or indefinite)... ]

if ∞/∞ =n than 0/0 =n how?"

Of course these are both true as ∞.n=∞ & 0.n=0...

If we talk strictly mathematics, we must keep in mind that infinity is not a number (belonging to the set of integers or real or whatever), therefore cannot take part in arithmetic expressions so lightheartedly like this. Otherwise, if we assume ∞ to be a number (a big big one indeed) then for example 0.∞ = 0 as an algebraic requirement. I'm talking about REAL 0 here, not just a small small number. To say that 0.∞=n we have to admit that infinity is something beyond just a huge number, or maybe that this 0 is not exactly 0 but a symbolic representation of an infinitecimally tiny number. So, are we talking mathematic or symbolic language?

Likewise, to say that ∞/∞ =n yields ∞.n=∞ is not as obvious as it seems at first glance, as in order to pass from the one equation to the other we need to multiply both sides of the first one by ∞, i.e. ∞.∞/∞=∞.n and I wonder how the annihilation will go on to give the ∞ = ∞.n (after all ∞.∞/∞ = (∞.∞)/∞ = ∞/∞ so we are back to where we started from!)

To keep the long story short, my point is that infinity cannot be handled like a normal number in strict mathematical sense. In fact, infinity is a symbol that takes us out of the awkwardness of n/0 as this expression is not strictly allowed.

Now, in practice, when we are about to explain various physical phenomena, we bump into expressions like this all the time, but they actually symbolically represent the final limit of a series of numbers. It is wise to know which phenomenon limits to an expression like this in order to have any clue.

And a final point . I doubt if there is a physical entity in the world that is infinite. (Of course I would like to have other opinions about this.) For example, are the points of the universe infinite? (I'm not talking about conceptual mathematical points.) If space is quantized (?), then there's no infinite here! Is it the speed that two distant coupled particles interact? Hmmm... I don't know.

Hi, Tasos...

"To say that 0.∞=n we have to admit that infinity is something beyond just a huge number, or maybe that this 0 is not exactly 0 but a symbolic representation of an infinitecimally tiny number. So, are we talking mathematic or symbolic language?"

Here I made a trial to manipulate REAL "0" & "∞" not a "tiny little number" and "not an incredible huge number"... But especialy the "0.∞" or "∞/0" seem to be really hard to be manipulated... Some tend to believe that both these two expressions are undentified... For example: 0.∞= "undentified" and this means that it is in accordance with my opinion that "n/0" has "no meaning" and is not permited... I tend to believe that «0.∞ = "undentified"» doesn't mean that «0.∞ = "indefinite"» because someone may claim that this could mean that 0.∞ = n (where n is any finite number) and this gives n/0=∞... And in my initial message I argued why I don't agree with this... I still believe that simply "n/0" has "no meaning"...

"Likewise, to say that ∞/∞ =n yields ∞.n=∞ is not as obvious as it seems at first glance, as in order to pass from the one equation to the other we need to multiply both sides of the first one by ∞, i.e. ∞.∞/∞=∞.n and I wonder how the annihilation will go on to give the ∞ = ∞.n (after all ∞.∞/∞ = (∞.∞)/∞ = ∞/∞ so we are back to where we started from!)"

I think that if you define i.e. that the proposition "A=B" is true then you are able to multiply both parts by "0" as it gives A.0=B.0 => 0=0 which is, also, true... In the same way it is permitted to multiply both parts by "∞" as it gives A.∞=B.∞ => ∞=∞ which is, also, true...

"..... (after all ∞.∞/∞ = (∞.∞)/∞ = ∞/∞ so we are back to where we started from!)"

Okay then... here it is: ∞/∞ = ∞.∞/∞ = (∞.∞)/∞ = ∞/∞ = (∞.n)/∞ = (∞/∞)^*.n = ∞.n

(* An "infinity" can include an indefinite number of "infinities" (or I should say "subinfinities"???), or even an "infinite" number of "infinities"... With the symbol "∞" I represent a "highest class infinity" which is "∞ = ∞.∞" ... So I think that this gives me the right to assume that: ∞/∞ = ∞ ... Infinity is a very tricky thing...)

Maybe, all these is nothing more than a trick (or even a cheat)...

But afterall: "∞.n=∞" is valid... Am I right???...

A reply to Tasos (#18):

I said before: "Okay then... here it is: ∞/∞ = ∞.∞/∞ = (∞.∞)/∞ = ∞/∞ = (∞.n)/∞ = (∞/∞)^*.n = ∞.n"

That was a big nonsense... (I didn't prove sth)...Let's try it again... You said that:

"..... (after all ∞.∞/∞ = (∞.∞)/∞ = ∞/∞ so we are back to where we started from!)"

So you say that: ∞/∞=n => ∞.∞/∞=n.∞ => (∞.∞)/∞=n.∞ => ∞/∞=n.∞

Hence the same nonsense as mine...

First of all we are trying to prove if "∞/∞=n => ∞=∞.n" or not... So you are not allowed to say that "∞.∞ = ∞" as this is sth that we don't know if it is valid... e.g. we don't know if "∞=∞.n" (or even "∞ = ∞.∞") because this is exactly what we are trying to prove (or not)... So we can not use this expressions in oder to get a result...

So, lets (both) forget all these things...

Lets just assume for now that "∞ = ∞.n" (or that "∞/∞ = n") for any kind of "infinity" where the n is any finite number (although I have some doubts that "∞/∞ = ∞" may be valid in general) ... I'll prepare another post in order to show why I believe that the above is correct... and I'll show some other interesting things...

Hi George,

"we don't know if "∞=∞.n" (or even "∞ = ∞.∞") because this is exactly what we are trying to prove"

Just a little reminder. Concepts, equations, etc. that contain ∞ can not be proven under any circumstances.

-John

A number line representing the placement of the numbers in pattern, such that zero is the assumed midway point, then there must also be an infinite number of negative integers to the left of the zero, as there are positive integers to the right of the zero.

So that infinity can not be reached in either direction, so that infinity minus infinity will not necessarily ever equal zero. Infinity is merely a descriptive term of a count of numbers, where it is possible that infinity is not necessarily equal to infinity, as a place number like one, two or three so that infinity added to a minus infinity does not necessarily equal zero, nor would infinity divided by infinity equal one. So an equation with a factor of infinity would never have an answer, as infinity is not placeable on any number line in either direction because you never can reach infinity by it's very definition.

Then negative infinity will always be less than zero and positive infinity will always be greater than zero?

joshua

I am so confused I lost count

Well said Joshua,

Zero is simply a point on a number line, or is it? Some say zero represents nothing. It can also be used as a place holder, as in 1,000, etc. It's also used as a starting point for something to take place, as in "start the stop watch now" (although the 1st thing you'll see on the display is 1, but by agreement the 1 must have followed 0; the beginning).

How about this. Since zero separates positive numbers from negative numbers can we ever cross from one to the other? This has been brought up before but I'll bring it up again since it's in the spirit of this thread (the old tortoise and hare thing). For example:

I'm a number line traveller, and I'm going along in a positive direction, say from +1 toward +2. However, there's a bungee cord attached to my rear that's being stretched and resisting my travel. Eventually, It becomes too much work to go on (I'm tired), so I relax and the bungee cord does what bungee cords do; it yanks me backward toward zero. Will I ever cross zero? If so, at what point? does it happen at .0000000000001... or somewhere else before I'm in negative territory?

Actually, I just gave it away. When I got tired and stopped, the zero marker on the number line just moved ahead to my position at that point. Bad example

So what it boils down to is that the number line is not absolutely fixed in space. It positions itself as needed for a particular occasion, right? In other words, it the above example, I become zero and external things (numbers) position themselves accordingly. If this is feasible, then when the number line shifts, does -∞ shift toward +∞?

-John

Assuming that the number line is flat and bidirectional is one assumption that I have trouble with. The world around us indicates a spherical relation in that the starting point is the center of a sphere in that zero may represent the our starting point of the center, allowing for an infinite number of rays radiating from that starting point expanding outward in an infinite range in a spherical manner, thus an infinite number of rays to an infinite number of points. It is that we assume that we are the starting point because of our view point, given the manner of infinity if our view point changed so would our placement of infinity and zero. Thus both terms are mere place holders for the point of view, and can not be calculated just estimated. So that [ N<0>N ] is always true.

joshua

"the starting point is the center of a sphere in that zero may represent the our starting point of the center, allowing for an infinite number of rays radiating from that starting point expanding outward in an infinite range in a spherical manner"

If zero is at the center of a sphere how do you account for positive and negative values? According to your statement, if all rays extend outward from the center of a sphere (zero) then, by your definition, they all are either positive, or they are all negative.

Everything above your plane is positive everything below your plane is negative, each ray is it's own number line with the arbitrary zero as the center. Again dependent on your position where the sphere expands out from to infinity.

joshua

"Everything above your plane is positive everything below your plane is negative"

Then if my plane is flying at 30,000 feet in a thunderstorm, all electrical charge below me is negative and all charge above me is positive, right?

Incidentally, is friction a positive, or negative, value on an inclined plane?

sure why not

joshua

why did I read all that? My head hurts. Is that what smart feels like?

Maybe thats why when a guy gets whacked on the thumb in the cartoons

he says "Wow that smarts"

cr3

Thanks (all of you) for your interesting ideas...

A new post will follow with some new thoughts as a "refreshment" of the discussion about the difficult concept of the "infinity"... I hope that it will be interesting...

Infinity is not a number, you have to turn it into a number before you can do any calculations. Furthermore, many nothings give you nothing. When does nothing become something? Once you have determine that, you will be able to find your solution.

Zero can not be divided by its self, that is why infinity is the measurement of 0+or-1.

If you go no farther than 1 then the balance of +1 is -1 this universe is complete as infinite to zero. Why is this so? Take any number divide it by 9 then divide by it's self then by 9 = 0.0 1234568. The sum of these are 29. add 1+2+3+4+5+6+8= 29 .

Notice that the 7 is never present. If you then add 29+7= 36. like the 7 missing in the first answer the 36 is missing a "0" to complete 360° as ∞.

Yes and 1 + 1 = 10

Johnjon

Most amusing that your mind can't see how words and numbers are related. 1=(5)and 5=(1) then what =(10)? 5+5 or 1+1.

Now take out your calculator please. I want you to see this is true. put in.

24/9/24/9= 0.0 1234568

42/9/42/9= 0.0 1234568

66/9/66/9= 0.0 1234568 INFINITE ORDER BY DIVISION

132/9/132/9= 0.0 1234568

264/9/264/9= 0.0 1234568

Now what does Zero have to do with this? well (0.0) is the only point in time that matter has no mass. But if you have no mass then you have no matter. the two zero's make the infinite universe. The dimension's became Linear 1 was now the infinite universt. (10.01) 10.01 is the mass of the infinite universe. the dimension's became Quadratic 2 was now the infinite universe. (210.012) 210.012 is the mass of the infinite universe. The dimension's became Cubic 3 was now the infinite universe. (3210.0123) 3210.0123 is the mass of the infinite universe. the dimension's became Biquadratic 4 was now the infinite universe. (43210.01234) 43210.01234 is now the mass of the infinite universe. The dimension's became Reciprocal 5 was now the infinite universe. (543210.012345) 543210.012345 is now the mass of the infinite universe. The dimension's became Modified Reciprocal 6 was now the infinite universe. (6543210.0123456) 6543210.0123456 is now the mass of the infinite universe. The dimension's became Generalized Reciprocal 7 was now the infinite universe. (76543210.01234567) 76543210.01234567 is now the mass of the infinite universe. The dimension's became Quartic 8 was now the the infinite universe. (876543210.012345678) 876543210.012345678 is now the mass of the infinite universe. the dimension's became Binomial 9 was now the infinite universe (9876543210.0123456789) 9876543210.0123456789 is now the mass if the infinite universe.

Now this is the prime infinite universe in order. when you used your calculator the answers you saw the seven never comes into view because the Modified Reciprocal and the Quartic are even numbers their power closes the infinite set. the Generalized Reciprocal and the Binomial are odd numbers their power open the infinite set. 6+8=14 (5) 7+9=16 (7) Six is between (5) (7) then your last infinite set would be 9+9=18 (9) Order is maintained through the Binomial's relationship with Zero. 9876543210.0123456789

GAW

"Most amusing that your mind can't see how words and numbers are related. 1=(5)and 5=(1) then what =(10)? 5+5 or 1+1."

No! There are number systems other than base 10. In binary (base 2) 1 + 1 = 10 or stated another way 1 + 1 = 0 with a carry... 1 2 4 8 16 32 ....

You lost me in the rest of that number dissertation.

-John

HI!

JohnJohn

^{UNIVERSAL ENGLISH}

_{^{1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 12}}

_{^{A B C D E F G H I J K L M N O P Q R S T U V W X Y Z}}

_{^{12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1 12 1}}

_{^{Y Z}}

_{^{ZY ∞ YZ}}

_{^{Z Y}}

_{^{To use line up A-L AND M-X The Y and Z are the Cartesian Cuordnance}}

_{^{ALL WORDS INTO NUMBERS AND NUMBERS INTO WORDS ATOMIC SCALE}}

I invented this system in 1980 how it came about was the a infinite relationship between words and numbers I discovered that the alpha and omega in the English language was balanced by a Cartesian cuordnance. Each letter has a specific weight or fractional value to make up words. when a word is used or assembled in the English language a placement is only correct if the meaning is rendered positive. The binary strength in a word is a infinite measurement that can never be changed. Just think that in the beginning was the word and the word was God. Remember this everyone beauty is in the eye of the beholder. The truth about ZERO is that the universe is beyond that thank God.

TO: G.K. you left your subject to soon your bones had just got a little meat on them. The things you seek to know have answers beyond your wildest imagination trust me. Infinity doesn't have a measurement it's beyond time.

Watch the stock market crash.

CAOSS is a word.

GAW

Hi cr3,

You could very well be right (there are biblical connotations in that squirrelly post)

As I said earlier, I got lost at "HI" in that numbers dissertation. Wonder if he caught on to 1 + 1 = 10?

-John

Guys, we are in front of an example of what meddling too much with zero and infinity can cause to your mind's sanity.

I recalled Douglas Adams, who in one of his books mentioned a machine on a certain planet which was able to expose you to the meaning of infinity, the vastness of the universe and consequently the nothingness of your being. It had the power to make you really understand all these. It was the worst think that could happen to you, no wonder it was used as the utmost punishment inflicting device. Now, I don't remember whether the unfortunate convicts eventually died, but even if they didn't, I guess that experience would have tremendous irreversible consequences on their brain cells and their psyche in general.

I didn't understand anything... ... What are you trying to show???...

Anyway, this whole entry [The Mysteries Of The Numbers "Zero" And "Infinity"] didn't give any specific and reliable answers... just interesting questions... So, if you are interested in this issue take a look in my next entry [The Mysteries Of The Number "Infinity"] that I posted few days later (as a sequel of this post)... That is much more interesting (than this post)... So, in the post [The Mysteries Of The Number "Infinity"], beside the questions, some interesting results are arised from a discussion between Tkot and me (thanks to Tkot who is better informed and more versed in maths than me)... It just need some patience to follow and understand our thoughts... And this is pure maths... ...

I have not checked the other posts for this, but... While infinity is an absolute, there are different sizes of infinity.

According to set theory, there are infinities with greater and smaller populations. For example, the set of all integers is infinite, however, the set of all real numbers is considered a bigger infinity because it contains more members.

Whacky, isn't it!!!

Hi Vermin. Yes, you are right. It's sth that I, also, mentioned at the end of my presentation of this issue (when I said about "infinities of different sizes"). If you have time take a look at my other entry "the musteries of infinity-part2" (see my post #33 above) which, in fact, is a sequence of this entry. (In "the musteries of infinity-part2" Tkot talks about "aleph" and a very interesting discussion follows between me and him which clarifies many things.) Is, by far, much more interesting than this entry (if you are interested in such issues of course)... ...