$\newcommand{\defeq}{\mathrel{\mathop:}=}$

## 2007/04/08

### 0^0

Some textbooks leave the quantity 00 undefined, because the functions x0 and 0x have different limiting values when x decreases to 0. But this is a mistake. We must define

x0 = 1, for all x,

if the binomial theorem is to be valid when x = 0, y = 0, and/or x = -y. The theorem is too important to be arbitrarily restricted! By contrast, the function 0x is quite unimportant. (See [220] for further discussion.)

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HTML 對程式碼（in particular C++ template code）和數學式實在不友善，尤其是後者！XD

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