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#1 2006-10-10 06:58:44

espeon
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Registered: 2006-02-05
Posts: 2,586

hmmm a mathamatical problem which has something to do with !!

in another topic devante said something about 5!! so i said is 5! is 120 then would 5!! be equivilent to 120!? i dont get it...someone help me


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#2 2006-10-10 07:02:58

luca-deltodesco
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Registered: 2006-05-05
Posts: 1,470

Re: hmmm a mathamatical problem which has something to do with !!

well for example


if you think of factorial as a function, then youre repeating the function again

so like



Last edited by luca-deltodesco (2006-10-10 07:06:56)


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#3 2006-10-10 07:05:56

espeon
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Re: hmmm a mathamatical problem which has something to do with !!

o so i was right. YAY!


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#4 2006-10-10 07:08:39

Devantè
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Registered: 2006-07-14
Posts: 6,400

Re: hmmm a mathamatical problem which has something to do with !!

Read luca-deltodesco's bottom part of post #2 for more information.

EDIT: Oh, and I said that 5!! = 120! originally, long before you made that post. tongue

Last edited by Devanté (2006-10-10 07:09:33)

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#5 2006-10-10 07:28:31

polylog
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Registered: 2006-09-28
Posts: 162

Re: hmmm a mathamatical problem which has something to do with !!

I wonder if any of you know for certain.. what is the correct order of multiple nested exponentiation:

For example luca wrote:

In this case the order does not matter:

Because of the funny property x^y = xy  for x = 2, y = 2.

However, for a number like:

We can interpret this as either either:

Or:


(number too large for windows calculator)

So which one is meant when no parentheses are used ?

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#6 2006-10-10 07:44:55

espeon
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Re: hmmm a mathamatical problem which has something to do with !!

hmm i dont wanna think of 120! because 100! alone is over 160 000 digits lol or thats what ganesh said at least


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#7 2006-10-10 07:46:21

luca-deltodesco
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Re: hmmm a mathamatical problem which has something to do with !!

with no brackets around exponentials, you go in order of bottom to top

so


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#8 2006-10-10 07:52:56

Devantè
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Re: hmmm a mathamatical problem which has something to do with !!

espeon wrote:

hmm i dont wanna think of 120! because 100! alone is over 160 000 digits lol or thats what ganesh said at least

Way off. 100! has an immense amount off digits less that 160000. tongue

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#9 2006-10-10 11:20:08

polylog
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Registered: 2006-09-28
Posts: 162

Re: hmmm a mathamatical problem which has something to do with !!

luca-deltodesco wrote:

with no brackets around exponentials, you go in order of bottom to top

so

Thanks. I'm not sure why I was thinking it is actually the other way around.. for example when evaluating:

It might seem natural to square the x first, but then the curve would be all wrong!

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#10 2006-10-10 11:48:49

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

Re: hmmm a mathamatical problem which has something to do with !!

I think it's the other way around. x^y^z = x^(y^z), unless otherwise bracketed.

If people wanted to write (x^y)^z, they could just as easily write x^yz.


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#11 2006-10-10 11:55:04

polylog
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Registered: 2006-09-28
Posts: 162

Re: hmmm a mathamatical problem which has something to do with !!

I guess I see now my confusion came from the "bell curve" function

which is not equal to:

because of the negation.  smile

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#12 2006-10-10 12:03:21

polylog
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Registered: 2006-09-28
Posts: 162

Re: hmmm a mathamatical problem which has something to do with !!

mathsyperson wrote:

I think it's the other way around. x^y^z = x^(y^z), unless otherwise bracketed.

If people wanted to write (x^y)^z, they could just as easily write x^yz.

Hmm, right! So i'm confused again.

Using the idea of evaluating the most deeply nested function first, if we for example in the case of the function i mentioned write:

Then the x^2 must be evaluated first because it then is an argument to the exponential function!

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#13 2006-10-10 12:09:37

Ricky
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Registered: 2005-12-04
Posts: 3,791

Re: hmmm a mathamatical problem which has something to do with !!

mathsyperson wrote:

I think it's the other way around. x^y^z = x^(y^z), unless otherwise bracketed.

If people wanted to write (x^y)^z, they could just as easily write x^yz.

I disagree.  a + b + c is considered (a + b) + c.  Note that there may be times when addition is not associative (although at the moment, I can't name one).  In the same way, I would say x^y^z is (x^y)^z.

Either way, it's pretty ambiguous and in such cases, you should use () to specify.


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#14 2006-10-10 22:03:40

Patrick
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Registered: 2006-02-24
Posts: 1,005

Re: hmmm a mathamatical problem which has something to do with !!

Devanté wrote:
espeon wrote:

hmm i dont wanna think of 120! because 100! alone is over 160 000 digits lol or thats what ganesh said at least

Way off. 100! has an immense amount off digits less that 160000. tongue

100! =
93326215443944152681699238856266700
49071596826438162146859296389521759
99932299156089414639761565182862536
97920827223758251185210916864000000
000000000000000000

158 digits


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#15 2006-10-10 22:08:25

Devantè
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Registered: 2006-07-14
Posts: 6,400

Re: hmmm a mathamatical problem which has something to do with !!

Because 9.33262154 × 10^157, right? tongue

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#16 2006-10-11 13:20:21

fgarb
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Registered: 2006-03-03
Posts: 89

Re: hmmm a mathamatical problem which has something to do with !!

is conventionally taken to be a^(b^c), not (a^b)^c. This convention was probably chosen because it makes it easier to simplify some expressions. For example, it allows you to write:

Incidentally, n!! is sometimes taken to mean n(n-2)(n-4)... , which is definitely not the same as (n!)! It's probably pretty rare to see it used this way though. smile

See http://mathworld.wolfram.com/DoubleFactorial.html

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#17 2006-10-11 14:21:27

George,Y
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Registered: 2006-03-12
Posts: 1,379

Re: hmmm a mathamatical problem which has something to do with !!

5!!=5*3*1 instead of = (5!)!

n!! is a useful notation in Wallis Equation, which is used to derive the Normal Curve in probability.


X'(y-Xβ)=0

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