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

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

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

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

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**Chaotic Neutral****Member**- Registered: 2005-10-31
- Posts: 55

Debating is good.

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

As at night, we realise we will never Know and further thinking is pointless....Yet we start again and again

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**Jims****Member**- Registered: 2005-11-28
- Posts: 42

Ah, imagination ...

Where is it you imagine the limits of imagination are?

Until the moment we perceive directly the borders of conceivabilty, thoughts are limitless.

While we tend to be bound to processing information based on our experiences and observations, the function of combining and reconstituting those ideas is limited only from times relentless march.

However, with time ... change allows us to output our theories and gives us oppurtunity to have new, yet unseen discoveries. Allowing fresh insight and renewed input for our contemplations.

Debating on the other hand, gets us nowhere. Unless people listen to each other. But that's where advantage comes into play, right? ... providing people talk (any amount greater than zero) ...

who's listening?

who's got plugs in their ears?

who's yelling?

who's whispering?

who's following?

who's leading?

Think about "SMELL!" (yell that and see how many sniffs you get) ...

even odors compete ... bacon versus roses ... that's about as far as my sense of smell goes. what's the relevance? I would argue a sense of smell is not important. Then again, I could walk into a gas filled room, notice nothing and pass out before I caught on. My limited smell recptors acclimatizing to the change in chemical surroundings without raising significant alarm.

*yawn*

∞ & 1/∞

Are the limits of numbers.

Being that they are limitless, they function as directional coordinates.

Constants.

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

What a poetic beginning!

But "debate" brings in the idea of "two opposing ideas, who wins?".

Perhaps "discuss" would be better? A good discussion can be enlightening for both parties.

And a truely smart person can revise his own thoughts after listening to others.

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

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**Jims****Member**- Registered: 2005-11-28
- Posts: 42

A feeble attempt to counterpoint "Debating is good".

Maybe the only real counterpoint is:

I agree.

*Last edited by Jims (2005-12-06 15:29:26)*

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**Chaotic Neutral****Member**- Registered: 2005-10-31
- Posts: 55

Maths is difficult.

Therefore, maths is difficult to master.(1)

Morons are stupid.

Morons do not understand the fact that boring and difficult things can be useful (relate boring as subjective to moron).(2)

This is a maths forum. (3)

Regarding 1,2,3 this is a moron-free forum.(4) (a moron will not want-be able to master maths)

A moron thinks he knows everything.

Therefore, a non-moron can admit that he lacks knowledge/understanding about something.(1*)

The point of debating=convince someone in a logical, rational or practically efficient way about the superiority of a certain opinion.(2*)

Regarding 4 and 1*, people here will listen to debating, and as we do consider improving ones knowledge and common sense good, and debating will work on this forum, I can allow myself to pull the conclusion that....

Debating is good. (please do not tell me about semi- demi- and quasimorons.)

*Last edited by Chaotic Neutral (2005-12-07 07:27:17)*

As at night, we realise we will never Know and further thinking is pointless....Yet we start again and again

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

He who knows not and knows not that he knows not is a fool; avoid him.

He who knows not and knows that he knows not is a student; teach him.

He who knows and knows not that he knows is asleep; wake him.

He who knows and knows that he knows is a wise man; follow him

Sanskrit saying

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

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**Chaotic Neutral****Member**- Registered: 2005-10-31
- Posts: 55

Interesting!

Now let's write that as a matrix.Who's in?

As at night, we realise we will never Know and further thinking is pointless....Yet we start again and again

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 20,371

Me!

|kn kn kn fool avoid|

|kn k kn student teach|

|k kn k sleeping wake|

|k k k wise man follow|

kn = knows not, k = knows

MathsIsFun, I knew this before. But I didn't know it was a Sanskrit saying.

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.

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**Jims****Member**- Registered: 2005-11-28
- Posts: 42

would that also apply to lions?

Because it might not be wise to wake a sleeping lion ... especially if he knows something.

or bears or dinosaurs ... though i'm not sure what a terrible thunder lizard would know ... how to be terrible, i suppose. in which case, definitely don't wake him!

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**Chaotic Neutral****Member**- Registered: 2005-10-31
- Posts: 55

Ganesh, how about this one:

1 2 rank

1 0 0 fool

2 0 1 student

3 1 0 asleep

4 1 1 wise man

statement 1=if he knows/knows not about the world

statement 2=is he knows/knows not about if he knows of knows not about the world

In the beginning I was confused, because I thought 3 factors were present but soon realised only 2 were.I have the idea I have missed something important in this one.

*Last edited by Chaotic Neutral (2005-12-09 04:50:23)*

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

You can use binary bits to represent:

1: has knowledge

10: is aware of own knowledge level

So:

0: knows not that he knows not

1: knows not that he knows

10: knows that he knows not

11: knows that he knows

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

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**Chaotic Neutral****Member**- Registered: 2005-10-31
- Posts: 55

To stay on topic, my new guess on 1/infinity would be

0,00000000000000000000000000000000000000000000000[infinite number of zeroes]000000000000001

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

I think you missed a couple of zeroes there!

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**Chaotic Neutral****Member**- Registered: 2005-10-31
- Posts: 55

Allright let's see who can write the most zeroes.

My attempt: 100!×(Length of Pi tail when written in size 24 expressed in tenths of nanometres) zeroes

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

[100!×(Length of Pi tail when written in size 24 expressed in tenths of nanometres)] +1 zeroes.

I win.

*Last edited by mathsyperson (2005-12-12 09:06:24)*

Why did the vector cross the road?

It wanted to be normal.

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

**igloo** **myrtilles** **fourmis**

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**Chaotic Neutral****Member**- Registered: 2005-10-31
- Posts: 55

What does it really mean?

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

Maybe I should have said that

**igloo** **myrtilles** **fourmis**

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**God****Member**- Registered: 2005-08-25
- Posts: 59

Infinity is meaninglessly large, so there's really no poing in wondering what 1/infinity is unless you're dealing in terms of limits. You can't divide by infinity because it's not a number. Just like I can't divide 1 by an elephant or an egg.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

You can in the right context.

Like, if you knew that a hen could lay 2 eggs in a day and wanted to work out how many days it had been in the henhouse if you found 10 eggs lying there.

10 eggs/(2eggs/day) = 5 days.

Why did the vector cross the road?

It wanted to be normal.

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**dritter85****Member**- Registered: 2009-06-23
- Posts: 1

if 1/infinity was 0 then we wouldnt exist. so its just an unfathomably small number.

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**1337ist****Member**- Registered: 2010-11-17
- Posts: 1

The answer is epsilon. I did much research into this recently, and all answers said it was infinitesimally small, and the term for that is epsilon. It's a Greek letter that looks like an E.:)

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,903

Hi 1337ist;

I know of at least one other forum that agrees with you.

I do not agree. I have seen it defined as less than a very small number. Here is how the physicists think about it.

Hurkyl wrote:

Infinity isn't a uniquely defined concept. There are many ways to include infinity (infinities) into a number system, each with their own properties.

The most common one is the example plus gave of the extended real numbers; in that system 1 / infinity is defined simply to be zero, because that's the choice that gives the right answer for the applications for which the extended real numbers were invented.

Other number systems behave differently. 1 / infinity is undefined for any infinite quantity in the ordinal number system. In other transfinite systems each infinite value has a unique nonzero reciprical (an infinitessimal).

Interestingly Mathematica, Maple, Derive and Mupad ( I know because I think I helped put it there ) will evaluate 1 / ∞ = 0. This is because in practical problems you would be thinking in terms of the limit.

To me 1 / ∞ is meaningless. I do not like the idea of it equaling a very small number. For computational sake one could consider it 0. That is why the math packages define it that way.

When I am forced to think about it, I think about it in terms of limits, then it equals 0.

http://mathforum.org/library/drmath/view/62486.html

http://mathcentral.uregina.ca/QQ/databa … evan1.html

I like this one best. In our number system the question is improper.

Stuart Anderson wrote:

It seems that every time someone constructs a number system that includes infinity, they get not just one, but a whole lot of different infinite numbers. So the answer to the original question "what is 1/infinity" is that...

---in the standard system:

"you can't ask that."---in the nonstandard system and the surreals:

"it will be one of the nonzero infinitesimal numbers, which infinity did you have in mind?"

How about this one?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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