0^0=?

樓上：
本人認為閣下的答案是錯的！
閣下有理據支持嗎？
a^0=1是必須在a不等於0的情況下
正如a/b也必須有一個先決條件:b不等於0
a^0=1的原因如下:
a^b/a^b=a^(b-b)=a^0
同時a^b/a^b=1
所以a^0=1
但是,當a=0時就不一樣了
a^b=0
則a^b/a^b=0/0
在數學上是undefined的
即未被定義的
為何0/0未被定義?
正如,你要找出一堆數的平均數
0個人的身高總共是0cm
其平均高度是0/0 cm
即是任何高度都可以
其實即是廢話
0可以是0的a倍
其中a的集合是C(複數的集合)
是所有數都可以的
在數學上是未被定義的

2006-12-27 19:04:53 補充：
設0/0=alog a=log 0-log 0由於log 0是未被定義的所以log a未被定義所以a未被定義

all the answer is1

you may think that

a^0 = a/a =1

so whatever the number is it, _^ 0 must equal to 1

2006-12-27 20:55:18 補充：
.......看錯la0^0 =error0^a=0................我都唔知

a^m^÷a^n^=a^m-n^(1)
如果m=n，∵a^m^= a^n^，∴a^m^÷a^n^=1
按照(1)這條公式，∵m=n，∴a^m-n^=a^0^
∵a^0^=a^m^÷a^n^=1
∴a^0^=1
由於a可代表任何數字，所以任何數字的0次方都等於1。

e.g. 2^2 = 4
2^-2 = 1/2^2 =1/4
2^2 x 2^-2 = 2^(2-2) = 2^0
4x(1/4) = 1
2^0 = 1


0的0次方是 Error?

令Y=0^0
所以有log 0 Y=0
利用換底公式有
logY
------ = 0 (換做10為底)
log0


但由於log0是不可能的,或者叫作不存在
原因:
令Z=log0
即10^Z=0
這是顯然不可能的(如要嚴格解釋,或許要用上集合論,這樣麻煩了)
所以log0不存在
因此log 0 Y=0 不存在
推出0^0不存在




I think it should be the problem of indeterminate form
what mean of indeterminate for is that we cannot find the exact range.
for example:
0/0
We cannot consider it by simple concept:
We cannot divide zero to zero part as there has nothing originally.
We consider as a part of limit which mean that we divide a very very very small part from a very very very small number.

for :
1/1=1, 1/0.1=10, 1/0.01=100, 1/0.000000000000000000001=1000000000000000000000

such that 1/0 will tend to infinite

similly 0/1will tend to 0

for 0/0 we cannot find exact number as tend to zero is only a concept.
0/0 can be very large or very small.

for your question
0^0=0^(1-1)=0^1/0^1=0/0
it is equal to 0/0 which is indeterminate


undefine is not equal to indeterminate
e.g.∞ is undefine but not indeterminate.

For othe indeterminate form, there is
∞-∞, 1^∞, ∞^0, 0/0, ∞/∞, 0*∞.

你個問題，好有問題

0^0=1 ,因為所有數的0次都是1

0^a=0 {a一要大過1} 如果a係0 答案會係１

a^0=1 <<<<<<一定

2006-12-27 18:07:25 補充：
a^0=1 一定 對

2006-12-27 19:45:16 補充：
樓下,你好強我 無修附數 我查過0^0=1無法計算我在修正[a^0=1 一定 對 ]a^0=1 A不可以=0 一定 對