Is there any way I can 'undo' the factorial operation? JUst like you can do squares and square roots, can you do factorials and factorial roots (for lack of a better term)?   Here is an example: 5! = 120.  Is there a way I can work out the number that must be factorialed (??) to give the answer 120?
I don't want to do this through trial and error, and the best way I have found so far was to start dividing from 1.     $n! = \text {a really big number}$   Ex. $n! = 9999999$   Is there a way to approximate n or solve for n through a formula of some sort?  Update (Here is my attempt):  Stirling's Approximation: $$n! \approx \sqrt{2 \pi n} \left( \dfrac{n}{e} \right ) ^ n$$  So taking the log:     $(2\cdot \pi\cdot n)^{1/2} \cdot n^n \cdot e^{-n}$       $(2\cdot \pi)^{1/2} \cdot n^{1/2} \cdot n^n \cdot e^{-n}$       $.5\log (2\pi) + .5\log n + n\log n \cdot -n \log e$       $.5\log (2\pi) + \log n(.5+n) - n$   Now to solve for n:     $.5\log (2\pi) + \log n(.5+n) - n = r$       $\log n(.5+n) - n = r - .5 \log (2\pi)$   Now I am a little caught up here.
What is wrong with my date regex? Leaflet Customer Marker Changes Position with Scale Why square the difference instead of taking the absolute value in standard deviation? In the definition of standard deviation, why do we have to square the difference from the mean to get the mean (E) and take the square root back at the end? Can't we just simply take the absolute value of the difference instead and get the expected value (mean) of those, and wouldn't that also show the variation of the data? The number is going to be different from square method (the absolute-value method will be smaller), but it should still show the spread of data. Anybody know why we take this square approach as a standard?  The definition of standard deviation:  $\sigma = \sqrt{E\left[\left(X - \mu\right)^2\right]}.$   Can't we just take the absolute value instead and still be a good measurement?  $\sigma = E\left[|X - \mu|\right]$ How to get the current time in Python How to check if a column exists in a SQL Server table? Possible Duplicate:          I live in a small apartment building and we can catch each-others wifi networks. We have different service provides and were wondering if we could amalgamate our networks so that we could use each others bandwidth transparently.   I would assume this would reduce latency.  Does anybody have a tutorial on how to fuse together wifi networks for a throughput increase? The target machine is a Linux computer.   EDIT  My work makes me do lots of 1TB flat file-transfers, so I believe my motivation is sound. JavaScript get clipboard data on paste event (Cross browser) My understanding is that when using a Bayesian approach to estimate parameter values:   The posterior distribution is the combination of the prior distribution and the likelihood distribution. We simulate this by generating a sample from the posterior distribution (e.g., using a Metropolis-Hasting algorithm to generate values, and accept them if they are above a certain threshold of probability to belong to the posterior distribution). Once we have generated this sample, we use it to approximate the posterior distribution, and things like its mean.   But, I feel like I must be misunderstanding something. It sounds like we have a posterior distribution and then sample from it, and then use that sample as an approximation of the posterior distribution. But if we have the posterior distribution to begin with why do we need to sample from it to approximate it? Is there a Ubuntu sanity check? Is there a standard procedure to 'unit test' an Ubuntu system against the deb packages?  Assume, a system has ubuntu-desktop installed according to the package manager. Can I find out, whether the file system has all the files in ubuntu-desktop and dependencies?   related question: Using modulo operation to draw graph Proving an entire, complex function with below bounded modulus is constant. How would I show that an entire function $f$ with the property $|f(z)| \geq 1$ must be constant?    I'm aware of Liouville's theorem, just not sure how to apply it here. How do I generate the upper triangular indices from a list? Is it correct that "etc." can not be used together in a sentence with "for example" and "such as"? I just read an article from a Chinese website for English teaching which mentions  that point. For instance, one can't say:     "I can play quite a few musical instruments, for example, the flute, the guitar, the piano, etc.".    The correct one should be:     "I can play quite a few musical instruments, for example, the flute, the guitar, and the piano."    Is it possible to find any references to prove that? I used to use a lot ctrl+alt+numpad to move windows, how can I use this feature on ubuntu 18 like it was default before?  Thank you in advance Bash scripts ran from from gnome/nautilus don't have environment variables I'm looking for a specific scifi book that I read years ago, I only partially remember the story, and I don't remember the author or the title.  What I remember of the story is:   An alien race picks up a signal from humans that includes instructions on how to make their own humans (genetic instructions). The humans grow up knowing they are created and are taught by the alien race. They are eventually given resources to build a ship, and go looking for their origins. They eventually find the solar system, but nobody answers. They find some stations orbiting earth and find that the station is very old, so old in fact that humans have long been extinct and other creatures have reached local space, and have been looking around the station as an archeological dig. I think they refer to two developed races from earth, but one developed from rats.   If anyone know what story this is, and can point me at it, its been driving me crazy for at least 15 years, and I think it's actually been much longer, since I can't remember when I read it. How does SQL Server handle logins when the user is a part of multiple groups with various privileges? I'm trying to wrap my head around how SQL Server decides to grant certain rights based on a users login privileges.  If a user is part of a group "READ ONLY" which has access to DB1, but they are also a part of a group "SysAdmin" which has full db owner rights to the same DB1, which rights are they given when they log in?  On a similar note. What if they are part of a group but also have a standalone account with other middle of the road privileges? Automotive electronic circuit design, Voltage divider to uC ADC pin Automotive Circuit requirement:   If input pin is connected to Battery(T87 line), the output of the circuit shall provide a output voltage of 5V to ADC pin of microcontroller, if the input pin is connected to GND, the output of the circuit shall provide a output voltage of 0V to ADC pin of microcontroller and if the input pin is left floating, the output of the circuit shall provide a output voltage of 2.5V to ADC pin of microcontroller.   The battery voltage in load dump condition could be up to 60V, but in normal operation without any fault condition, it would be up to 32V.  Would a simple voltage divider (with a pull-up to 5V) with a blocking diode be enough? Any other ideas? What parameters of the ADC of the microcontroller should be considered? Injection current into the uC- ADC pin would be critical, right? How do I find out the voltage thresholds? Also, what are the parameters of the Schottky diode that I should look to select? The diode would decouple the input pin from the centre tap of the voltage divider, because in case the input pin is connected to battery, the injection current into the uC ADC pin would be too high.  I have used a switching diode, since it was already available in the Bill of Materials. How can I clone an ArrayList and also clone its items in Java?  For example I have:  ArrayList&lt;Dog&gt; dogs = getDogs(); ArrayList&lt;Dog&gt; clonedList = ....something to do with dogs....   And I would expect that objects in clonedList are not the same as in dogs list. Double-column listing package Not too well up on LaTeX, but I want to use the listings package for listings spanning a two-column format.  Unfortunately, asterisks cannot save me (like for figures/tables); this doesn't work:  \begin{lstlisting*} ... \end{lstlisting*}   I've Googled about, but got no satisfactory answer, and getting a bit desperate. Should be simple... hope I'm not missing something stupid. Perhaps it's possible to embed this into a separate spanning float?  Help?  (P.S., I've posted this on the main stackoverflow site as well...  if this is considered a duplicate, please comment and I'll remove the other. Getting a bit desperate fighting a deadline.)