1waffle1
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| Joined: 16 Oct 2007 |
| Total Posts: 16381 |
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| 29 Oct 2011 02:22 PM |
+ is the opposite of - * is the opposite of / x^y is the opposite of x^(1/y)
What's the opposite of a factorial? A factorial really isn't a mathematical function, it has limitations, you can only do it when the argument is a positive integer. |
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| 29 Oct 2011 02:31 PM |
| Nothing. What can you think of that the opposite of a factorial could do? |
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1waffle1
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| Joined: 16 Oct 2007 |
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| 29 Oct 2011 02:32 PM |
720? = 6 No real purpose that I can think of. |
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pwnedu46
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| Joined: 23 May 2009 |
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| 29 Oct 2011 02:35 PM |
| Since factorials are recursive multiplication (n! = n * (n-1) * (n-2) * ... * 1), the opposite of that would be recursive division. I don't think there's a specific name though. |
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Aaaboy97
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| Joined: 05 Apr 2009 |
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| 29 Oct 2011 02:35 PM |
>x^y is the opposite of logₓ(y)
There is no defined opposite of a factorial, considering how you would need lookup tables to find the reverse. |
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1waffle1
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| Joined: 16 Oct 2007 |
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pwnedu46
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| Joined: 23 May 2009 |
| Total Posts: 7534 |
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| 29 Oct 2011 02:40 PM |
"x^y is the opposite of logₓ(y)"
No. x^y = z is the opposite of logₓ(z)=y
ex: 3^5 = 243 log base 3 of 243 = 5 |
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Aaaboy97
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| Joined: 05 Apr 2009 |
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| 29 Oct 2011 02:45 PM |
oh oops, sorry about that
I've just barely began to learn about logarithms, and it's all from my own experimentation |
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pwnedu46
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| Joined: 23 May 2009 |
| Total Posts: 7534 |
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| 29 Oct 2011 02:48 PM |
| @aaa: Lol. Actually, I was about to post the same thing, but then I was lik wait...that's wrong. :3 |
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Varp
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| Joined: 18 Nov 2009 |
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| 29 Oct 2011 03:59 PM |
They're called inverses. They're denoted as f^-1, if f is the function being inverted.
f^-1(f(x)) = x
Also, with the whole thing about exponents, the inverse of with a constant a:
f(x) = x + a f^-1(x) = x - a
f(x) = x * a f^-1(x) = x/a
And then, with exponents, it has two inverses, as it isn't commutative. You have the two functions:
f(x) = x^a f^-1(x) = x^(1/a)
f(x) = a^x f^-1(x) = log_a(x)
For the factorial function, you have the function:
f(x) = x * f(x-1) f(1) = 1
While I'm not entirely sure how you would find a recurrence relation to express the inverse, you can just use the process of:
function inverseFactorial(x) local r = 1 local v = 1 while v < x do r = r + 1 v = v * r end if(v ~= x)then error(x .. " is not in the range of the factorial function.") end return r end
This is basically a trivial implementation of an inverse; it just uses the property of g(f(x)) = x and tests various f(n) until f(n) equals the argument passed to the inverse function. This process must always terminate since n! monotonically increases & has a discrete domain
(Also, you could look up the gamma function; while your answer then would be gamma^-1(x) which is... probably not easy to compute. It also only works on certain domains) |
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NXTBoy
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| Joined: 25 Aug 2008 |
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| 29 Oct 2011 04:43 PM |
| You might want to take a look at the [gamma function](http://en.wikipedia.org/wiki/Gamma_function) |
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pwnedu46
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| Joined: 23 May 2009 |
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| 29 Oct 2011 05:53 PM |
| @NXT: uhh...wikipedia didn't help. |
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