One divided by Infinity

abhishek_rttc · 2005-07-25 20:16:31

Yah, I was expecting this question.
The explanation of value of infinity/ infinity is as following :-

Rule (a) suggests that the value of this fraction should be infinity
and the rule (b) suggests that the value of this fraction should be zero; hence we get a contradiction and the values suggested by numerator and denominator can't be made to agree.

In this case we arise to a conclusion that the value of this fraction
infinity/infinity is indeterminant.

Some other indeterminant forms can be quoted as:
0xinfininy and 0/0

Obiviously the second one fraction quoted above involves a no., i.e. 0, which is very well known to us and none can question its existence and still this fraction 0/0 is indeterminant.

One more thing, these indeterminant forms are very useful in higher maths and a very important L'Hospital Rule for finding limits is applicable only when a fraction is in indeterminant form 0/0 or inifinity/infinity.

abhishek_rttc · 2005-07-25 20:20:29

And as for these rules (a) and (b) is concern, these can be assumed as basic postulates related with concept of inifinity

Jai Ganesh · 2005-07-25 20:32:22

The logic seems acceptable.
It is easy to say 1/∞ is 0 because 1/0 is ∞,
just as 1/(a/b) = b/a.
If 1/a=b, it follows that 1/b=a
Indeterminate forms are only when both a and b are equal to zero,
or both a and b are equal to infinity.
Abishek, you missed another indeterminate form.
That is 0^0

Last edited by Jai Ganesh (2005-07-26 00:05:01)

eleusis · 2005-08-01 19:47:09

1/x;x->∞;1/x=0

one divided by x, as x approaches infinity. The limit is equal to zero.

Thisisthe4thdimension · 2005-10-29 11:46:57

ok infinity is a concept and not a number it refers to something infinantly large, but it is used in math for limits ex: lim 1/oo x -> oo equals 0 if you use abs(F(x)-L)<e and x>n. it is also the basis for the theroy that we live in the forth dimension.

the 0 dimension has 1 point oo^0=1
the 1st dimension is a line with an infinant amount of points oo
if you run a line through every point of the 1st dimension you get a plane so you have infinity more points per point which is the same as oo^2
if you put a line through every point on the plane you get volume and and since there are infinity more points per point in the 3rd you get oo^3
so the 4th dimension would have to make 3d space infinatly larger (oo^4 points)and time does that since there isnt a limit to time making each point, but this is just a theroy and it doesnt matter any way. considering time to be a dimension is just tecniality and i doubt any scientific discoveries will result in seeing it one way or the other.

also please dont tell me i cant spell to save my life i already know that tks

Danial Newman Abbet · 2005-11-06 11:46:11

Seeing as your working in theory rather than reality you can create a forth spatial dimension if you wish to - I'm just finishing off a piece on Tesseracts, which are, roughly speaking, the 4d equivalents to cubes.

∞, as you say, is a concept not a definable, numerical constant. If ∞ were treated as a number then mathematics basically starts to break down - ∞ is the largest number there is and cannot increase, so ∞*2 is the same as ∞*1. If 1X=2X then X isn't a number - it's either ∞ or 0.

I read an interesting site that tried to describe the enormity of ∞ - Things like that any number, no matter how huge or beyond the scope of the human mind to perceive (I think it gave 3^^^^3 as an example), is still closer to 0 than to infinity. I'd give a link, but my browser wiped all my bookmarks a few months ago so I'm not sure where the page is. (The site itself was about technological singularities basically, when we have the technology to make ourselves smarter. When were smarter well know how to make ourselves smarter still in a shorter time, and once weve done that well be smart enough to make ourselves even smarter. You get the picture. Essentially an exponential increase in human intellect, which would eventually tend to infinity, causing what the author described as ascension.)

martian · 2005-11-21 23:34:07

eleusis is right

the lim(1/i) as i → ∞ = 0

what I really what to know is, what is 0/0 ???? heheheh that will stump a lot of you.
I can think of 4 possiblilities

1.
0 over anything is 0 thus 0/0 = 0

2.
anything over 0 = ∞ thus 0/0 = ∞

3.
anything over itself = 1 thus 0/0 = 1

4.
As a combination of the above 3 rules 0/0 = any and every number in exsistance including imaginary numbers

Jims · 2005-11-28 23:33:46

An artists perspective on math:

0/0 = 0
when nothing is absolute

0/0 = ∞
when something between nothing is everything

0/0 = 1
when zero is unique

0/0 = any and all real or imaginary #s
when spontaneous generation exists

1/∞ > 0
when everything excludes nothing

∞/∞ = 1
except when;
∞ ≠ ∞

How about -∞ (negative infinity)?
Subtracting infinity, would that be equal to zero or with the difference of its co-additive(s)?
or is it simply included as a part of inifinity itself?

Chaotic Neutral · 2005-11-29 07:03:19

You cannot divide by infinity as you cannot divide by 0. These two are each others opposite, and everything else is a compromiss between the two

MathsIsFun · 2005-11-29 08:54:51

Hi Jims, and welcome to the forum ... I really like:

"0/0 = any and all real or imaginary #s
when spontaneous generation exists"

because that is part of my theory of the universe!

Chaotic Neutral · 2005-11-29 09:09:44

There isn't anything spontaneus, randomity is relative to the starting values (ask me for more details I don't like annoying people with my theories)

Jims · 2005-11-29 23:15:40

"randomity is relative to the starting values"
to what extent?
i doubt anyone here get's annoyed by theories

Think i'll start compiling a list a of philosophical math formulas:
0-∞
0/∞
∞*0
0^∞

Chaotic Neutral · 2005-11-30 00:40:17

When the white ball hits the triangle of the colored balls in snooker, a common man will say that the course of the colored balls will be "random", while a physician will calculate exactly how the balls will go if all factors (force, angle, .... ....) are given.

The word "random" is a relative term in probability mechanics, meaning that in a closed algorithm, the choice/action of a factor would be randomly determined.Because we don't have the means, time, and neccesivity to calculate every movement of the person's brain particles determining his choice, we could call his choice random.

But there are still begin values, such as the force, air/table resistance, angle, ball weight, ball surface cleanness, .. ... ... in the case of the snooker table.
On a global scale, the "initial push" values can not be tracked back without some sort of supercomputer.But they exist.Therefore, 0/0 could not contain spontaneously chosen numbers, only [spontaneus disregarding the initial values] or [according to initial values]
Because we are talking highly theoretical math here, we cannot disregard anything, hence no random numbers possible.

My theory:

1/0=∞ (as the amount of points on a line is infinite, so is the amount of nothings infinite in 1.So it is in 2,3,... but I guess we could speak of ∞², ∞³ ....)

0/0=1 (as there is only one point for 0 on a x,y axis table, as there is only one point in a point, one line in a line, so there is only one nothing in nothing.)

0/1=0 (no substance could be in nothing)

∞/0=∞ to the power of infinite(infinite in place of the ²)

0/∞=this one is hard. according to primary logic it's 0, but who knows....

correct me if I made mistakes

Jims · 2005-12-01 06:26:23

Suppose, inifinity is a single number that is the sum total of every number, and that there is no limit to the number of numbers.

Directly we could compare inifinity to zero, as they are opposites in that zero is the sum absence of any number.

Indirectly, dividing everything by it's components, the only way to split it, and keep track of the size of any of it's pieces ...
each 1/∞ would equal anywhere from the smallest possible number above zero ("primary logic" says that is what 1/∞ defines), or to inifinity itself *; necessarily, referencing the range of the component (numerator in relation to surrounding points or comparable elements).

example:
digital waveform
time - pitch - volume - frequency - shape
given zero for volume ... how many zeroes? if not the whole of time, then the NUMBER of zeroes becomes absolutely relevant. From that perspective, zero (as a constant), given multiple measurable qualities, requires the record of it's reference points.

and so,

0/∞ = inifinite zeroes

unless "primary logic" dictates the use of only one dimension at all times.
i'm guessing you meant;
"according to the single scope of numbers themselves"

*(seeing as with zero being a limit, and infinity having no limit, there should be two inifinities ... inifinitely large and infinitely small ... large being the common interpretation, language is tricky.)

This is ignoring "negative numbers". Standard use of negative numbers, as i understand it, present zero as a reference item. This readily presupposes the number zero as a set-up starting point rather than a value ... any value it is given is created as reference for the intended parameters measured. In my interpretation then, "negative numbers" themselves are wholy man-made and mainly used for pre-judged interpretation of values in relation to the reference. Common sense tends to point us in the same direction though.

to the Earth, is UP towards or away from the Sun? does Earth have an UP?

and so,
what are we looking at?
how much?
how many?
how many different things?
how many same things?
what kinds of things?

what is the resolution of our perception?

what is the quantity of parameters?

Chaotic Neutral · 2005-12-01 08:51:16

Interesting points.But check this out:

Infinity is not a number, infinity could indeed be endlessly small.For example, Pi:

An endless number, yet every digit that comes is smaller than the former.0,1 is smaller than three, 0.4 is smaller than 1... This means, if Pi would be drawn on an axis (how is that called in english, that orthonormal thing with the (x,y) it's lenght would constantly grow into infinite smallness, meaning it could never grow past the previous digit (the 0.1 could never grow beyond the 3) but still it would grow forever.

"Standard" infinity is everything, 0 is nothing.How could we explain 1?

And about those negative numbers: imagine a axis set (or how it might be called).Imagine us living in the I quadrant of the goniometric circle (+,+), for us only the positive things (matter, one-way at one time movement, one-way at a time time course) is possible.
On the same goniometric circle (or ball, regarding our would is (x,y,z)) there is a II quadrant (-,+) a third being the complete opposite of ours and a forth (+,-).
0 is the nothing in the middle, and different everythings in every direction....

And sorry, I could not answer the UP question because I don't know what an UP is.
And please explain the last group of questions, don't really understand them.

And I worked with 2 or 3 dimensions.

Last edited by Chaotic Neutral (2005-12-01 09:10:14)

Jims · 2005-12-01 23:32:04

UP ... is directional ... but only in relation to established norms.
your mouth is presumably DOWN from your eyes ... and eye-brows are generally considered UP from the eyes.
what if you stand on your head? or look UP? then UP changes ... or does it?
is UP in relation to ones body or in relation to the ground (the Earth)?

is UP, the direction opposite of the net gravitational force affecting an object at point "zero"?
for me, UP would then be a direction quite different from the UP of someone on the other side of the globe. to the Earth (as a body) ... is there an UP ? or would there be infinite "UPs" radiating into space ... ? or is the Earths UP, the singular direction opposite the Sun? or is there no UP for the Earth, because it is an orbital body?

depending on the interpretation, there could be infinite or one or zero UP classifications.
therefore, it's important to keep in mind, in any determination of characteristics:

what are we defining?
for what purpose?
how many dimensions / parameters are we defining?
what are the definitions of the related parameters and how do they relate?

arguably, definitions of a single word can vary depending on the application.
like i said, language is tricky.

Chaotic Neutral · 2005-12-02 04:08:06

Sorry, you writing up in capitals confused me, thought it was some sort of an abbreviation.

Languages aren't tricky but outdated.They are made for everyday communication and are less used for relations of parameters.

So...
Up can be: direction opposite to the direction of gravity, if the object according to which up is defined lies in the direct (non-orbital) contact to the field of gravitation.

Spacemen have no up, so does earth not have an up according to the sun as earth orbits it, it does not stand on it.
Me standing on earth (or any other gravity-giving celestial) does have an up, everything further from the celestial than I am is above me, and the direction from the celestial to it is up.As celestials are balls, the gravity is transmitted according to the form, therefore something further from the celestial on the opposite side of the celestial is still up.

Hence, up is strictly gravity-related.

Jims · 2005-12-02 07:24:49

says you! ha!
... try looking up "up".

on the other hand,

1/∞ aproaches, but never quite goes up to zero.

... or is it down to zero?

languages aren't at all outdated ...
... words ... said ... mean ... things ... ugh!

languages are tricky in that there are multiple meanings for many words and therefore context is critical. speaking simply, languages need to evolve (and do) to suit our uses for communicating ideas and stuff. they are tricky because in order to properly create new meanings for words yet spoken we must follow parameters established by what has already been said, splitting infinitives here, to advancingly and prescriptively create useful, new context.

it computes, and is therefore proclaimed a "computer"
it looks like a mouse, let's call it a "mouse"
they speak! ... they call themselves "speakers"

in terms of the rate at which language changes versus the recent alarmingly fast rate of new technology in parallel with an evolving understanding of reality, the universe, etc. ...

still, you'd think we would have a word for the formula:

1/∞

try this angle;

looking up at ∞ we see the solar system, the galaxies, the whole of the cosmos ... and more, imaginably ...

looking down at 1/∞ we see the micro-organisms, the molecules, the atoms ... and less, perceivably ...

inifinity from our vantage point ...
+∞ as UP
-∞ as DOWN
strictly talking about size here.

or is that non-PC to short persons?

how about "ytinifini" ?
eh?!
any takers?
a bargain at twice the price!!!

yttrium88 · 2005-12-02 07:59:14

I think they often call 1/? infintessimal, try checking it out on mathworld (google mathworld, it's the first result).

The way I look at it:

f(x)=1/x

limit f(x) as 1->? is 0

This is especially true if we are applying 1/? in a prarical setting.

yttrium88 · 2005-12-02 08:00:28

hmm..i don't know why, but my infinity sign came out as a '?'

MathsIsFun · 2005-12-02 08:14:15

∞ use:

:infin

yttrium88 · 2005-12-02 08:21:02

Ok, thanks!

Here's the mathworld website:

http://mathworld.wolfram.com/Infinitesimal.html

mathsyperson · 2005-12-02 08:25:09

MathsIsFun wrote:

To make any of these work, put a ":" in front of the text.
alpha=α and=∧ ang=∠ asymp=≈ beta=β bull= cap=∩ cong=≅ cup=∪ deg=° Delta=Δ delta=δ divide=÷ empty=∅ epsilon=ε equiv=≡ exist=∃ fnof= forall=∀ frac12=½ frac14=¼ frac34=¾ gamma=γ ge=≥ harr=↔ hArr=⇔ infin=∞ int=∫ isin=∈ lambda=λ laquo=« larr=← lArr=⇐ le=≤ mu=μ nabla=∇ ne=≠ ni=∋ notin=∉ nsub=⊄ omega=ω oplus=⊕ otimes=⊗ part=∂ Phi=Φ pi=π plusmn=± prime=′ Prime=″ prod=∏ prop=∝ radic=√ raquo=» rarr=→ rArr=⇒ rho=ρ Sigma=Σ sigma=σ sim=∼ sube=⊆ sub=⊂ sum=∑ sup1=¹ sup2=² sup3=³ supe=⊇ sup=⊃ tau=τ there4=∴ theta=θ times=× xi=ξ zeta=ζ

Last edited by mathsyperson (2005-12-04 04:04:24)

Roraborealis · 2005-12-04 03:29:24

Wow, look at all this debating over a simple statement!

Chaotic Neutral · 2005-12-04 03:56:55

Debating is good.

However, as our brains are limited, we will never truly understand anything beyond it's limits.

Math Is Fun Forum

#26 2005-07-25 20:16:31

Re: One divided by Infinity

#27 2005-07-25 20:20:29

Re: One divided by Infinity

#28 2005-07-25 20:32:22

Re: One divided by Infinity

#29 2005-08-01 19:47:09

Re: One divided by Infinity

#30 2005-10-29 11:46:57

Re: One divided by Infinity

#31 2005-11-06 11:46:11

Re: One divided by Infinity

#32 2005-11-21 23:34:07

Re: One divided by Infinity

#33 2005-11-28 23:33:46

Re: One divided by Infinity

#34 2005-11-29 07:03:19

Re: One divided by Infinity

#35 2005-11-29 08:54:51

Re: One divided by Infinity

#36 2005-11-29 09:09:44

Re: One divided by Infinity

#37 2005-11-29 23:15:40

Re: One divided by Infinity

#38 2005-11-30 00:40:17

Re: One divided by Infinity

#39 2005-12-01 06:26:23

Re: One divided by Infinity

#40 2005-12-01 08:51:16

Re: One divided by Infinity

#41 2005-12-01 23:32:04

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#42 2005-12-02 04:08:06

Re: One divided by Infinity

#43 2005-12-02 07:24:49

Re: One divided by Infinity

#44 2005-12-02 07:59:14

Re: One divided by Infinity

#45 2005-12-02 08:00:28

Re: One divided by Infinity

#46 2005-12-02 08:14:15

Re: One divided by Infinity

#47 2005-12-02 08:21:02

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#48 2005-12-02 08:25:09

Re: One divided by Infinity

#49 2005-12-04 03:29:24

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#50 2005-12-04 03:56:55

Re: One divided by Infinity

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