52 Factorial

Kosmiche

Kosmiche

Kosmiche

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All you maths boffins will already know about this, but to those that aren't maths boffins have you heard of 52 factorial?

Basically its the number of all the different ways a ordinary pack of 52 playing cards can be arranged.

It is a big number...

80,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Stephen Fry explaining further

 
I like how the sum of integers from 1 to infinity = -1/12. And it's not even too hard to explain, most would understand a simplified explanation.
 
tbyeah said:
I like how the sum of integers from 1 to infinity = -1/12. And it's not even too hard to explain, most would understand a simplified explanation.
Click to expand...

x = 1+2 +3+4+5+6+....
Multiply both sides by 4
4x = 4 + 8 + 12...

Subtract 4x from x
-3x = 1-2+3-4


Then with some trickery that I forget:p
-3x= 1/4

So x = -1/12.

Mathematicians just take the pee really:D
 
Eames said:
It is a big number...

80,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
Click to expand...

It's approximately 8.0658e67....

80658175170943878571660636856403766975289505440883277824000000000000
 
tbyeah said:
I like how the sum of integers from 1 to infinity = -1/12. And it's not even too hard to explain, most would understand a simplified explanation.
Click to expand...
Well it's not really the case that 1+2+3+4+... converges to anything, let alone -1/12.

The point is that there is a function, call it Z(s), whose values happen coincide with the value of the sum 1/1^s+1/2^s+1/3^s+... when s>1, i.e.

Z(s) = 1/1^s + 1/2^s + 1/3^s +... when s>1. (*)

When s<=1 the values of Z(s) are determined by completely different sum and putting s=-1 into this sum we find Z(-1)=-1/12. If we *pretend* that -1>1 so that (*) is valid when s=-1 then we get

-1/12 = Z(-1) = 1/1^{-1} + 1/2^{-1} + 1/3^{-1} + ... = 1+2+3+...

But we're only pretending -- the expression on the right doesn't converge! :)
 
tbyeah said:
I like how the sum of integers from 1 to infinity = -1/12. And it's not even too hard to explain, most would understand a simplified explanation.
Click to expand...

it doesn't technically. They're basically just assigning a value to an infinite series.
 
Lightnix said:
1. Somehow. I think it's just one of those things where they conveniently define it like that rather than for any particularly good reason.
Click to expand...

well if you look at it in terms of sets of n numbers - number of ways to arrange them....

{1} can be just {1} so 1
{1,2} can be {1,2} or {2,1} so 2

etc...

how many ways can you order the empty set? {}

just 1: {}
 
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