Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,608

What is 1 / Infinity ?

Is it 0 ?

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

Offline

**Zach****Member**- Registered: 2005-03-23
- Posts: 2,075

1/infinity? Infinity contains all known numbers, including negative numbers, in existance... Thus, you can really divide it by 0, can you?

Boy let me tell you what:

I bet you didn't know it, but I'm a fiddle player too.

And if you'd care to take a dare, I'll make a bet with you.

Offline

**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,608

Inifinity. A number SO BIG that you can't ever reach it.

Some people say it is the number that is equal to the largest number you can think of plus one.

So, we know what 1/10 is, we know what 1/100 is, we know what 1/1,000,000,000 is (one billionth), but what is 1/Infinity?

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

Offline

**Zach****Member**- Registered: 2005-03-23
- Posts: 2,075

Oh! Oh! 1/2?

Boy let me tell you what:

I bet you didn't know it, but I'm a fiddle player too.

And if you'd care to take a dare, I'll make a bet with you.

Offline

**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,608

Only if Infinity=2 ... it don't

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

Offline

**Zach****Member**- Registered: 2005-03-23
- Posts: 2,075

... That was the joke. O.o

Boy let me tell you what:

I bet you didn't know it, but I'm a fiddle player too.

And if you'd care to take a dare, I'll make a bet with you.

Offline

**Zach****Member**- Registered: 2005-03-23
- Posts: 2,075

Alright. I've been thinking (Ragnarok!) and I've come up with this;

1/infinity = 0? X

Infinity is -not- a number, thus a mathmatical symbol cannot do anything to it. Neither is a variable, it's a concept (For example, you're not going to have 1/law, are you?). Thusly, infinity is not a number, but it is a concept, thus cannot be used in such a way.

But, if you're using infinity as a short-hand version of a long number, a really really long number, then express it like so;

x = The Overall number.

Infinity = (x+1) Continuously.

That's not too clear, but I'll try and clean it up. X is a number, say 5. You have 5 people + 1 person you have 6. x stands for the number of people you have, thus you go back to the start and you x+1 again to get 7 people and you loop it.

To show off my QBasic cleverness, here it is in a machine language;

REM START

$x=0

Do

x=$x

$x=x+1

Loop

END

- In all technicalities that'd work.

So, taking that you mean Infinity in that way, 1/infinity would be infinitesimally small, not 0.

I bet you didn't know it, but I'm a fiddle player too.

And if you'd care to take a dare, I'll make a bet with you.

Offline

**Roraborealis****Member**- Registered: 2005-03-17
- Posts: 1,594

MathsIsFun wrote:

So, we know what 1/10 is, we know what 1/100 is, we know what 1/1,000,000,000 is (one billionth), but what is 1/Infinity?

One infinitieth!

School is practice for the future. Practice makes perfect. But - nobody's perfect, so why practice?

Offline

**justlookingforthemoment****Moderator**- Registered: 2005-05-26
- Posts: 2,161

See http://mathforum.org/library/drmath/view/62486.html (click link)

*Last edited by justlookingforthemoment (2005-05-29 22:11:07)*

Offline

**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,608

And what you wrote in code, Zach, is called an "infinite loop" (though no such loop has ever gone on for infinity, at least not as fas as I know! )

Offline

**Zach****Member**- Registered: 2005-03-23
- Posts: 2,075

Yes. There's actually no point of the END, as I've added no loop exit factor.

I bet you didn't know it, but I'm a fiddle player too.

And if you'd care to take a dare, I'll make a bet with you.

Offline

**Mr T****Member**- Registered: 2005-03-30
- Posts: 1,012

that's great i hope u had fun

I come back stronger than a powered-up Pac-Man

I bought a large popcorn @ the cinema the other day, it was pretty big...some might even say it was "large

Fatboy Slim is a Legend

Offline

**Roraborealis****Member**- Registered: 2005-03-17
- Posts: 1,594

Well, I did.

School is practice for the future. Practice makes perfect. But - nobody's perfect, so why practice?

Offline

**stewie****Member**- Registered: 2005-03-28
- Posts: 820

haw haw ho

HAPPY HAPPY, JOY JOY

Fatboy Slim is the band of the 90s, thats if you want to call it a band because its really a one man name

Offline

**I love pi****Member**- Registered: 2005-06-30
- Posts: 11

I think it should be 1 infinitieth or just plain 0.

Offline

**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,608

1 infinitieth gets my vote!

Can't be zero. Becasue that would mean that an infinite number of zeros would make one, and I have tried multiplying zero by some pretty big numbers and it is always zero

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,357

In mathematics, 1 divided by zero is consrued to be infinity.....

There's a reason for that; when 1 is divided by an extrememly small number, like

0.00000000000000000000000000000000000000000000000000000000000000001,

the resultant is a very big number.

On the other hand, When 1 is divided by an extremely large number, say a centillion,

the resultant is so small that it is almost zero, repeat ALMOST zero, not zero....

But what happens when we divide 1 by a number as big as infinity?

The result is zero.

When 1 is divided by an infinitely large number, the result is an infinitely small number,

and when this infinitely small number is added to itself infinite number of times,

the result would be exactly 1, not any more.

This is difficult to prove, but the logic behind it is perfectly okay.

If you are interested in knowing more about infinity,

use any search engine and get information about

Hilbert's Hotel.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**Roraborealis****Member**- Registered: 2005-03-17
- Posts: 1,594

How can infinity exist???

School is practice for the future. Practice makes perfect. But - nobody's perfect, so why practice?

Offline

**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,608

Wow, this kind of conversation is usually reserved for Buddhist Monks sitting on the side of mountains in the Himalayas.

The Existence of Infinity.

I guess if you can imagine it, then it exists, at least in your mind.

Offline

**Roraborealis****Member**- Registered: 2005-03-17
- Posts: 1,594

MathsIsFun wrote:

Wow, this kind of conversation is usually reserved for Buddhist Monks sitting on the side of mountains in the Himalayas.

LOL !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

I suppose there's no other way of it existing because every number is impossible to see, and is all in the mind.

School is practice for the future. Practice makes perfect. But - nobody's perfect, so why practice?

Offline

**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,608

Infinity is not one of the "Real" numbers (ie it is not a 3 or a 7.01, or even a -1/7th), but nonetheless we can still use it.

For example:

y = 5 - 1/x

What happens as x -> inifinity? Answer: y -> 5.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,357

Yes, you are right. Infinity is diffuclt to comprehend for others, not for mathematicians.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

**kylekatarn****Member**- Registered: 2005-07-24
- Posts: 445

Zach wrote:

To show off my QBasic cleverness, here it is in a machine language;

REM START

$x=0

Do

x=$x

$x=x+1

Loop

END

that would probably result in "overflow error" =P

Offline

**abhishek_rttc****Member**- Registered: 2005-07-25
- Posts: 6

Let's consider the problem to findout the value of 1/infinity.

Here the numerator doesnot suggest any specific law to findout the value of the fraction and a fraction, having numerator as 1, can take any possible value whether fininte of infinite,

Now we consider the denominator, i.e., infinity. There are some specific rules to find out value of an expression having infinity as a term:-

a) If infinity appears in the numerator the fraction takes the value infinity

b) If infinity appears in the denominator the fraction takes the value zero.

Here rule (b) about infinty suggests that the value of this fraction 1/inifnity should be zero and the numerator 1 expesses the possibility of this value and there is no contradiction between the result obtained.

Hence the value of 1/inifinity must be zero.

Offline

**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,608

abhishek_rttc wrote:

a) If infinity appears in the numerator the fraction takes the value infinity

b) If infinity appears in the denominator the fraction takes the value zero.

Ahhh ... but who came up with the rules?

And what is infinity/infinty ? Does rule a) or b) apply?

Offline