Originally posted by XanthosNZ This relationship is normally stated as e^i*pi = -1.
You can find a good basic explanation here:
http://www.math.toronto.edu/mathnet/questionCorner/epii.html
Does the e^(ix) = cosx + isinx observation get you there? x=pi isn't the only point on the line where cosx=-1 and sinx=0. What about where x=3pi? cos(3pi) + isin(3pi) also =-1. so does e^(ipi) = e^(3ipi)?
Originally posted by deriver69 One answer is because it works, but if you think of factorials as being the number of ways of arranging that many objects, there is only one way of arranging zero objects.
because it works Ahh, the obverse side of the coin which reads "We Haven't the Foggiest." Sounds conclusive enough to fool 'em everytime!
Originally posted by deriver69 One answer is because it works, but if you think of factorials as being the number of ways of arranging that many objects, there is only one way of arranging zero objects.
Um, there are no ways to arrange zero objects. You are into semantics if you state that because there is no way to arrange zero objects then that "no way" can be re-written as "one way"
The only truth is to state there are zero ways to arrange zero objects.
Originally posted by FreakyKBH Howzabout a whole lot of zero's? Surely they cannot amount to nothing.
Since Infinity - 1 cannot be a finite number (no finite number plus 1 can equal infinity), then:
Infinity - 1 = Infinity
And one could subtract infinity from both sides, then multiply by -1, to conclude that 1 = 0. Now, with a lot more zeros you can begin to see how they will amount to quite a lot.
Originally posted by XanthosNZ The factorial is mearly a mathmatical construct. 0! is defined just as the definition of a prime number is made to ensure that 1 is not one.
0! is part of a larger axiom that states that empty products are equal to one, just as empty sums are equal to zero.
Originally posted by uzless Um, there are no ways to arrange zero objects. You are into semantics if you state that because there is no way to arrange zero objects then that "no way" can be re-written as "one way"
The only truth is to state there are zero ways to arrange zero objects.
0!=1 should be re-visited.
The only way of arranging zero giraffes on my kitchen table is the way I have zero giraffes on my kitchen table at the moment. There is no other way of arranging zero giraffes on the table.
On another point mentioned earlier, 1 not being a prime number is consistent with the definition of prime numbers being numbers with only 2 factors (1 has one factor).
Search "empty product" on Wikipedia for a nice explanation. By the way, in response to Bowmann, infinity - infinity is an indeterminate form, therefore the operation can't be performed.
Originally posted by deriver69 The only way of arranging zero giraffes on my kitchen table is the way I have zero giraffes on my kitchen table at the moment. There is no other way of arranging zero giraffes on the table.
On another point mentioned earlier, 1 not being a prime number is consistent with the definition of prime numbers being numbers with only 2 factors (1 has one factor).
Well said.
However, 1 could have an infinite number of factors: each 1.
Originally posted by Ramiri15 By the way, in response to Bowmann, infinity - infinity is an indeterminate form, therefore the operation can't be performed.
20 Jul '06 05:56
To Mathematicians
Back to Top