推 herstein:存在...自己可以找出來(-f)(x)=-f(x) 01/02 16:06
※ 引述《Jer1983 (stanley)》之銘言：
: Let K be a compact subset of R^n, and let C(K) be the collection of all
: real-valued functions on K.
: For f,g ε C(K) define: (f+g)(x) = f(x) + g(x) and (f*g)(x) = f(x)*g(x)
: for xεK.
: Show that ( C(K), +, *) is a commutative ring with identity. But it is not
: an integral domain.
: thanks in advance.
驗證 C(K) 是否存在 additive inverses 的時候:
for f in C(K) there exists -f in C(K) such that f + (-f) = (-f) + f = 0.
我要問的是:
-f 存在嗎? 因為題目並未定義 (c*f)(x) = c * f(x) for c in |R
題目只有定義 (f*g)(x) = f(x)*g(x).
thanks in advance.
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