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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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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)
The Beginning Of All Things To End.
The End Of All Things To Come.
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o so i was right. YAY!
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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.
Last edited by Devanté (2006-10-10 07:09:33)
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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:
So which one is meant when no parentheses are used ?
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hmm i dont wanna think of 120! because 100! alone is over 160 000 digits lol or thats what ganesh said at least
Presenting the Prinny dance.
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with no brackets around exponentials, you go in order of bottom to top
so
The Beginning Of All Things To End.
The End Of All Things To Come.
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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.
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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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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.
Why did the vector cross the road?
It wanted to be normal.
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I guess I see now my confusion came from the "bell curve" function
which is not equal to:
because of the negation.
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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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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.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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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.
100! =
93326215443944152681699238856266700
49071596826438162146859296389521759
99932299156089414639761565182862536
97920827223758251185210916864000000
000000000000000000
158 digits
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Because 9.33262154 × 10^157, right?
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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.
See http://mathworld.wolfram.com/DoubleFactorial.html
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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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