Re: [中學] 國中說的「零次函數」
※ 引述《linijay (Ajay)》之銘言：
: 零次函數指的是f(x) = k，k≠0
: 我一直以為它有這個名字是因為它相當於f(x) = k(x^0)
: 昨天有人問了我才想到，k(x^0)在x=0處沒有定義耶....
: 那請教為什麼叫零次函數呢？謝謝
f(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_0, where a_n≠0
we call f(x) a polynomial of degree n, NOT function
^^^^^^^^^^
and denote deg(f)=n
then we have deg(f*g) = def(f) + deg(g) .........(1)
that is why we call f(x)=k, k≠0, a polynomial of degree 0
However, f(x)=0 is NOT a polynomial of degree 0
because it cannot satisfy eq. (1)
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◆ From: 123.194.224.241
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yes,
i mean degree is naturally defined for n≧1
^^^^^^^^^
and we can use eq. (1) to generalize this definition
to n=0
This situation is very similar to the factorial.
we can naturally define n! for n≧1.
and we have
(n+1)! = n! (n+1) .....(2)
Hence, we can use (2) to generalize to the case n=0.
※ 編輯: JohnMash 來自: 123.194.224.241 (05/29 22:29)
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