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1) For the reason that you can't divide by zero, see my answer at http://answers.yahoo.com/question/index?…
2) 0! = 1, by definition. This is a matter of convenience, and using 1 works out well. For example, we want to be able to say that the number of combinations of n things taken k at a time is n! / (k!(n-k)! If k = n, the answer is logically 1, so if we define 0! = 1, this works well.
Similarly, if you list the sets you can form by taking n elements 0 at a time, there is only 1: { }, the empty set. So again, setting 0! = 1 makes sense.
If we want to say n! = n x (n-1)!, it's also is consistent to say 0!=1 so that 1! = 1(0!).
(To digress, it's like why we say 1 isn't a prime number. It doesn't have the nice properties that primes have, so we've arbitrarily (actually for good reasons) say it is not a prime, by convention.)
3) I was going to say that 0^0 is undefined. In many applications, it is. However, there are some situations were it is defined as 1. I was a bit surprised to find all the mathematical situations where this may be desired. For example, you may say that the general polynomial function =
p(x) = sum from i=0 to n of (a_i)x^i
What do we use for the term x^0 when x=0? We call it 1, and just say that p(0) = a_0
See the discussion at http://en.wikipedia.org/wiki/0%5E0#Zero_…
The key point is that 0^0 is very context dependent, so there's no one-size-fits-all answer.
http://en.wikipedia.org/wiki/0%5E0#Zero_…
2) 0! = 1, by definition. This is a matter of convenience, and using 1 works out well. For example, we want to be able to say that the number of combinations of n things taken k at a time is n! / (k!(n-k)! If k = n, the answer is logically 1, so if we define 0! = 1, this works well.
Similarly, if you list the sets you can form by taking n elements 0 at a time, there is only 1: { }, the empty set. So again, setting 0! = 1 makes sense.
If we want to say n! = n x (n-1)!, it's also is consistent to say 0!=1 so that 1! = 1(0!).
(To digress, it's like why we say 1 isn't a prime number. It doesn't have the nice properties that primes have, so we've arbitrarily (actually for good reasons) say it is not a prime, by convention.)
3) I was going to say that 0^0 is undefined. In many applications, it is. However, there are some situations were it is defined as 1. I was a bit surprised to find all the mathematical situations where this may be desired. For example, you may say that the general polynomial function =
p(x) = sum from i=0 to n of (a_i)x^i
What do we use for the term x^0 when x=0? We call it 1, and just say that p(0) = a_0
See the discussion at http://en.wikipedia.org/wiki/0%5E0#Zero_…
The key point is that 0^0 is very context dependent, so there's no one-size-fits-all answer.
http://en.wikipedia.org/wiki/0%5E0#Zero_…
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You can't divide by zero.
Anything to the power of zero is one. It just is, in high school I had a hard time conceptualizing that one too.
and 0! is undefined. think of 2! - that's 2 x 1, 5! = 5 x 4 x 3 x 2 x 1
How would you do 0!? You can't.
Anything to the power of zero is one. It just is, in high school I had a hard time conceptualizing that one too.
and 0! is undefined. think of 2! - that's 2 x 1, 5! = 5 x 4 x 3 x 2 x 1
How would you do 0!? You can't.
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1) 0/0 = undefined --> you can't divide any integer (including 0) by nothing
2) 0! = 1 (no idea why)
3) 0^0 = 1 --> 0^0 = 0^(n-n) = 0^n / 0^n = 1
2) 0! = 1 (no idea why)
3) 0^0 = 1 --> 0^0 = 0^(n-n) = 0^n / 0^n = 1
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cause it has no value
here check these websites
http://www.physicsforums.com/showthread.…
http://en.wikipedia.org/wiki/Division_by…
here check these websites
http://www.physicsforums.com/showthread.…
http://en.wikipedia.org/wiki/Division_by…
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1) you cant divide something by zero
2) dont get what you are asking
3) some say zero, some say 1, and some say undefined
2) dont get what you are asking
3) some say zero, some say 1, and some say undefined
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0! = 1 by definition.