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Discrete-Space Derivative

  • Thread starter WhiteRae
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  • #1
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I was looking up how to find the derivative of a factorial and found this thread:
https://www.physicsforums.com/showthread.php?t=1328

What is a discrete-space derivative? I tried looking it up, but had no luck. If someone could explain it in a way someone in calc 2 could understand that would be great, or at least point me in the direction of more information.
 

Answers and Replies

  • #2
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A discrete space is a space where all subsets are open. I have never heard of a discrete space derivative, however.

Have you heard of the gamma function? http://en.wikipedia.org/wiki/Gamma_function
Take a look at how it relates to the factorial function. It does take a lot of work to understand if you're only at the first year level in math.
 
  • #3
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I was looking at the Gamma Function. I understood it a little bit, but in general it was way over my head.
 
  • #4
gabbagabbahey
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What is a discrete-space derivative? I tried looking it up, but had no luck. If someone could explain it in a way someone in calc 2 could understand that would be great, or at least point me in the direction of more information.
The general idea is that the more familiar continuous space derivative,

[tex]\frac{df}{dx}=\lim_{\Delta x\to 0}\frac{f(x+\Delta x)-f(x)}{\Delta x}[/tex]

Can be generalized in cases where the smallest possible difference between two different values of a discrete variable [itex]x[/itex] is a constant (in other words, all elements of the set are equally spaced) [itex]\delta x[/itex] according to the equation

[tex]\frac{df}{dx}=\frac{f(x+\delta x)-f(x)}{\delta x}[/tex]

(For a continuous space, [itex]\delta x[/itex] is infinitesimally small)

If [itex]x[/itex] is only allowed to be a natural number, then the smallest diffence between two different values of x is 1, and so

[tex]\frac{df}{dx}=f(x+1)-f(x)[/tex]

Whether or not this is really the type of derivative you are interested in depends on the context of your problem.
 

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