7!^7!=

[RobLikesBrunch]

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Fuck yeah.

[TadMod]

I didn't understand the thread name for a minute, thinking it was something to do with those weird multi-character smilies made with text... then realised it's literal meaning... and loled SO HARD!

Seriously though, how did you figure this out? Write a program or something? I would laugh so hard if it turned out one number was wrong XD

[tokage]

http://www.wolframalpha.com/input/?i=7!^7!

Edit: The forum hates me...

[zoidberg rules]

can anybody tell me wtf just happened??

im not all that smart at the moment sooo...

[Untadaike]

The site spazzed out with the input 7!^7! for some reason.

[Endoperez]

can anybody tell me wtf just happened??

im not all that smart at the moment sooo...

It's math.
n! = n * (n-1) * (n-2) * (n-3) ... * 1

or,

7! = 7 *6 *5 *4 *3 *2 *1 , which is a big number

^ is the symbol for exponents. 7! ^ 7! means that you multiply 7! with itself 7! times. 7!*7!*7!*7!*7!...

which is a ridiculous number

[RobLikesBrunch]

I tried to do 9!^9!, but my browser kept locking up when I tried to paste in the result. I used Wolfram Mathematica to do the calculation. Also, you'll notice a large amount of 0s at the end of the number--I presume this is because, given the size of the number, we can approximate there. It's like having a 500 place decimal and throwing off the last 200 numbers as 0s. Edit: this is incorrect, refer below.


"9!" is pronounced "nine factorial" and as Endo has described, simply means 9*8*7*...2*1. Factorials are very important in statistics (even on things like the SAT, where they're used on permutation problems--if I have five snow globes how many different ways can I arrange them? The answer is 5!, or 120....and we can even do factorials of decimals using the gamma function: ) and they're often seen in series. For example, we can write trigonometric functions in terms of series, which feature factorials:


(while complex looking, these series are remarkably easy to derive and can be done using simple calculus)

This is actually how your calculator will calculate sin(x) (it will only use the first 4-5 terms...that's accurate to about ten decimal places or something). So sin(x) roughly equals x - x^3/3! + x^5/5! - x^7/7! where x is the angle in radians...and the factorials are interesting, because we can see them rapidly increase with each successive term, and as we are dividing by them (and factorials are more "powerful" than exponents), we can see that each successive term decreases in magnitude, such that as you go along, each term has "less of an impact" upon the final number, which is why we can approximate with only 4-5 terms.

This is actually how Euler's identity, e^i*pi +1 =0 can be proved.

Pi can also be calculated using the infinite series for arctangent, but--as you may suspect--each successive term because small very quickly, so we say the series converges slowly. To calculate pi we want a series that converges fast--i.e., gives us the most decimal places with the least amount of terms, so no one actually uses arctangent to calculate pi---there are more efficient series.

[Endoperez]

Woo, maths in English... I am almost certain I understood that.

[tokage]

I tried to do 9!^9!, but my browser kept locking up when I tried to paste in the result. I used Wolfram Mathematica to do the calculation. Also, you'll notice a large amount of 0s at the end of the number--I presume this is because, given the size of the number, we can approximate there. It's like having a 500 place decimal and throwing off the last 200 numbers as 0s.

The 0s are perfectly fine there. Every faculty over 5 has at least one trailing zero, because you have 5*2 = 10 in there as a factor. All over 10! have two zeroes, all over 15! have three.
7! = 5040 . When you exponentiate a given number, you could also exponentiate the factors of that number independently and get the same result, e.g. 20²=400=2²*10².
For our example that leaves us with 5040 ^5040 = 504 ^5040 * 10 ^5040. The 10 ^5040 is where all the zeroes come from. I haven't counted, but I guess there should be 5040 trailing zeroes, given that 504 only will generate 4 or 6 (4*4=16 4*16=64) as the last digit of the other factor (in fact no base without a trailing zero will give you a trailing zero).

Well, isn't it RobLikesBrunch trying to look flashy again.

[RobLikesBrunch]

I tried to do 9!^9!, but my browser kept locking up when I tried to paste in the result. I used Wolfram Mathematica to do the calculation. Also, you'll notice a large amount of 0s at the end of the number--I presume this is because, given the size of the number, we can approximate there. It's like having a 500 place decimal and throwing off the last 200 numbers as 0s.

The 0s are perfectly fine there. Every faculty over 5 has at least one trailing zeroe, because you have 5*2 = 10 in there as a factor. All over 10! have two zeroes, all over 15! have three.
7! = 5040 . When you exponentiate a given number, you could also exponentiate the factors of that number independently and get the same result, e.g. 20²=400=2²*10².
For our example that leaves us with 5040 ^5040 = 504 ^5040 * 10 ^5040. The 10 ^5040 is where all the zeroes come from. I haven't counted, but I guess there should be 5040 trailing zeroes, given that 504 only will generate 4 or 6 (4*4=16 4*16=64) as the last digit of the other factor.

Well, isn't it RobLikesBrunch trying to look flashy again.

http://www.purplemath.com/modules/factzero.htm

You're correct and I'm rather wrong--I like how you separated out the the 10^5040 in order to find the number of zeros. Clever.

[TheBigCheese]

Wait, is it just a number, or did the forum actually run the calculation because you put it in the title?

[Blorx]

As with TBC, I am lost.

[Assaultman67]

Wait, is it just a number, or did the forum actually run the calculation because you put it in the title?

He calculated the number using wolframalpha ...

Then he just pasted it ...

It would of been cooler if he proved an actually useful value such as pi or e rather than some random large number ...

[TheBigCheese]

Alright... so it's a large number. Couldn't he have just achieved the same result by stamping on his numpad for a few minutes?

[Assaultman67]

Yes! thats kinda why i don't get the point ...