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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,646

Two things are infinite: the universe and human stupidity; and I'm not sure about the universe.*Albert Einstein*

We must accept finite disappointment, but never lose infinite hope.*Martin Luther King, Jr.*

Nature is an infinite sphere of which the center is everywhere and the circumference nowhere.*Blaise Pascal*

The infinite! No other question has ever moved so profoundly the spirit of man.*David Searls*

There can not be more infinities than one; for one of them would limit the other.*Sir Walter Raleigh*

It is difficult beyond description to conceive that space can have no end; but it is more difficult to conceive an end. It is difficult beyond the power of man to conceive an eternal duration of what we call time; but it is more impossible to conceive when there shall be no time.*Thomas Paine*

To see a World in a grain of sand, And a Heaven in a wild flower, Hold Infinity in the palm of your hand, And Eternity in an hour*William Blake*

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

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

MathsIsFun wrote:

To see a World in a grain of sand, And a Heaven in a wild flower, Hold Infinity in the palm of your hand, And Eternity in an hour

William Blake

Without any prior knowledge, Lara Croft explodes into Blake's room and starts shooting at him yelling something about a Triangle of Light.

MathsIsFun wrote:

Two things are infinite: the universe and human stupidity; and I'm not sure about the universe.

Albert Einstein

What a great guy.

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.

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

so the dark dicussions forum has begun then

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

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,646

So it would seem ...

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

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

[Striking Chord]

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.

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

Dark disscusions... you picked the right name. Good work. Dark disscusions... ahh yes.

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

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

I feel very proud!

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

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 22,953

Definition:-

log (x) is denoted as log(1)x

log (log x) is denoted as log(2) x

log[log(logx)] is denoted as log(3)x

and so on.

We know that log of zero or a negative number is not defined.

My question is, for what value of n would log(n) ∞ i.e. log(n)infinity, be not defined?

(eg. log(6)Googolplex is not defined.)

Warning : We are moving from infinite to transfinite

*Last edited by ganesh (2005-08-11 23:58:36)*

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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**insomnia****Real Member**- Registered: 2005-03-23
- Posts: 944

It is impssible for the human mind... Nah- nah-nah-na-na-naaaaaaahhhh. Sorry. That song was on the radio whilst I was typing this.

Where was I? Ah yes.... to comtemplate infinity. Try thinking about a limitless about of anything. It is impossible, something always creeps in, without you noticing. The human mind is too advanced and yet, retarded. It's advanced in the way that we have words that we know what they mean, but cannot visulaise them. (That's the retarded bit)

Anyway, this last week I've been all on my own at work and...............the building is still standing and has been re-posessed. I'm so proud of my self *sniff*

Friends are angels who lift our feet when our own wings have trouble remembering how to fly

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,646

You got through the week without causing any major damage, embarrassment or financial loss????

Well done!

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

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,646

ganesh wrote:

My question is, for what value of n would log(n) ∞ i.e. log(n)infinity, be not defined?

So, you are asking about taking an infinite series of logs, starting with n, and hoping that you do or don't go ≤0 ... ??

Lets test it at n=2: log(2) = 0.301, log(0.301) = -0.521, log(-0.521) = undefined

So, for n=2 we did log three times and got an undefined

Lets test it at n=20: log(20) = 1.301, log(1.301) = 0.114, log(0.114) = -0.942, log(-0.942) = undefined

So, for n=20 we did log fourtimes and got an undefined

(BTW I used log10)

Is that the idea?

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**mathsyperson****Moderator**- Registered: 2005-06-22
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I think that's it, because ganesh's log(6)googolplex fits that.

log(0)googolplex=googolplex

log(1)googolplex=googol

log(2)googolplex=100

log(3)googolplex=2

log(4)googolplex=0.301...

log(5)googolplex=-0.521...

log(6)googolplex=undefined.

And none of that needed a calculator!

Why did the vector cross the road?

It wanted to be normal.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 22,953

Yes, I used logarithm to the base 10 for convenience.

The idea is to show that

Infinity + 1 = Infinity

Infinity + Infinity = Infinity

Infinity x Infinity = Infinity

Infinity ^ Infinity = Infinity

Infinity ^ Infinity ^ Infinity ^ Infinity ........Infinite times = Infinity

This is true because because we can never say for what value of n

log(n)infinity would be undefined.

And this is only the fourth stage of iteration (also referred to as 'tetration').

No wonder, Infinity is beyond comprehension for the human mind!

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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