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This is a place to ask questions about math terminology, and to post links to other resources out on the web.
Bruce Brantley
2004-08-28 13:37:20
! ?

I keep seeing the ! and other symbols (thank you Penny). It's pretty obvious to me that ! is a calculus function. I never went beyond Algebra and Geometry in HS(poor decisions in my Fresh year). I believe a full explanation would be way too long and too difficult for me to fully ingest, but I would like to get a general idea of what type of function is being applied to a number when adding the !. For example, when I see:

8!

I don't think it is like 8 times pi or the square root of two, where I would automatically know that the product of the two will be larger but an irrational number. Is it more like I'm taking 8 and putting it into a proven equation that will result in say an infinitely smaller number? Or is it more like plotting 8 on a two or 3 dimension graph.

I have been surfing for information, but unfortunately I have yet to find anything that will break it down slow enough for me to get.

SilverKnight
2004-08-28 14:01:04
Re: ! ?

It is called "factorial". It is defined for all non-negative integers, and is shorthand for multiplying by all the positive integers less than or equal to the argument.

So: 5! = 5x4x3x2x1 = 120
Also, 0! is defined as 1.

Note that this is a discrete (not continuous) function.

There is also the related "Gamma function" which you may be interested in.

Please see http://mathworld.wolfram.com/Factorial.html for more information.

Bruce Brantley
2004-08-28 18:13:56
Re: ! ?

SK,

You are really good. Thanks, many postings will make a lot more sense to me now. I am learning so many interesting things from this site. I'm even thinking about taking a calculus course, because my son starts HS this year. I would like to be able to help him in a couple of years when he gets to Calc.

Thanks again.

Gamer
2004-08-29 13:44:09
Re: ! ?

There's lots of math on the web it seems; the flooble community have been showing me all sorts of interesting things.

Bruce Brantley
2004-08-29 14:46:30
Re: ! ?

Gamer,

Yeah, I keep finding sites, but they barely stay basic long enough for me to follow. This is going to take a while. Today I was reading about the Riemann Theory. Way over my head and yet quite interesting. Then it occurred to me that if Riemann could be proven, it would prove the Goldbach conjecture. The funny thing is that 3 weeks ago I never even heard of the Goldbach conjecture. I think Levik did a good job with this site.

SK,

Just read your "And Levik said, "let there be Flooble"" bit. It was worth a good laugh.

Bruce Brantley
2004-08-29 17:09:25
Re: ! ?

SK,

OK it took a while, but I think I got it. The factorial ! is actually the positive integer portion of the gamma function. The gamma function also includes complex numbers like the sqrt -1 and negative integers. An example of the gamma function is:

Gamma Function = (n-1)! = -1*-2*-3*-4 .... looks like to infinity

Bruce Brantley
2004-08-29 17:35:55
Re: ! ?

I forgot to say if n = -1

and if n = 6 then we are back to your original factorial !

But if n = sqrt3 is it then

Gamma Function = sqrt2 * 1 which is just the irrational # sqrt2

Brian Smith
2004-08-30 07:49:08
Re: ! ?

Take a look at http://mathworld.wolfram.com/GammaFunction.html

Bruce Brantley
2004-08-31 22:48:16
Re: ! ?

Thanks Brian,

But I read that page. Then re-read numerous times. The above is what I deduced from that web page. Apparently I was incorrect, if you re-referred me to that page. Don't worry about though. I picked up a Calculus book yesterday. Worked my way through chapter 1 already. I'll get the Gamma Function before long. You guys aren't here to teach me Calc. But I may ask for clarification of terms some times. Thanks again.

Mike Graham
2004-09-06 23:12:16
Re: ! ?

Factorial is not a particularly calculus related concept, and has many applications in even non-calc-based probability/statistics.

Kudos for going through so much work to help your son, that is really admirable,

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