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#1 2005-06-11 23:50:05

MathsIsFun
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Registered: 2005-01-21
Posts: 7,534

Ah Yes, Infinity

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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#2 2005-06-13 01:50:02

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

Re: Ah Yes, Infinity

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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#3 2005-06-13 08:31:26

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

Re: Ah Yes, Infinity

so the dark dicussions forum has begun then


I come back stronger than a powered-up Pac-Man big_smile
I bought a large popcorn @ the cinema the other day, it was pretty big...some might even say it was "large
cool Fatboy Slim is a Legend cool

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#4 2005-06-13 10:20:18

MathsIsFun
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Registered: 2005-01-21
Posts: 7,534

Re: Ah Yes, Infinity

So it would seem ...


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

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#5 2005-06-13 12:50:51

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

Re: Ah Yes, Infinity

[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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#6 2005-06-17 05:14:33

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

Re: Ah Yes, Infinity

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


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

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#7 2005-06-17 05:26:50

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

Re: Ah Yes, Infinity

I feel very proud! big_smile


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

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#8 2005-08-11 23:54:58

ganesh
Moderator
Registered: 2005-06-28
Posts: 13,239

Re: Ah Yes, Infinity

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 cool

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


Character is who you are when no one is looking.

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#9 2005-08-12 00:23:09

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

Re: Ah Yes, Infinity

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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#10 2005-08-12 10:33:07

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,534

Re: Ah Yes, Infinity

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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#11 2005-08-12 10:44:51

MathsIsFun
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Registered: 2005-01-21
Posts: 7,534

Re: Ah Yes, Infinity

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?


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

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#12 2005-08-12 11:00:34

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

Re: Ah Yes, Infinity

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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#13 2005-08-12 17:11:20

ganesh
Moderator
Registered: 2005-06-28
Posts: 13,239

Re: Ah Yes, Infinity

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!


Character is who you are when no one is looking.

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