co-domain vs range

2009-12-19 11:29 pm
Let f: {1, 2} -> {3, 4, 5} be a function defined by
f(1) = 3 and f(2) = 5.
Find the co-domain of this function.

According to the definition in Hung Fung Pure Maths textbook, the answer should be {3, 5}.
However, my textbook says that the answer is {3, 4, 5}.

I wonder if my textbook is wrong?!
{3, 4, 5} should be the range, not the co-domain.

Anyone here can explain which is right? Thanks.
更新1:

To myisland8132: Hung Fung (Calculus I) p.5: Let f: A -> B Then f[A]: {y: y = f(x) for some x in A} is the codomain of f and f[A] is a subset of B. So, Hung Fung is wrong?

回答 (1)

2009-12-20 12:38 am
✔ 最佳答案
range 指由 domain 的元素通過 function 實際形成的元素的集合。co-domain 指 function 的值域。明顯地﹐co-domain 包含 range﹐反之則不然。一般地﹐當沒有明白指出時﹐一個函數的 range 和 co-domain 會當成相等。






圖片參考:http://www.mathsisfun.com/sets/images/domain-range-codomain.gif

所以原題目的co-domain 是{3, 4, 5}, range 是 {3,5}。不過我覺得Hung Fung Pure Maths textbook 應該不會寫錯﹐是不是您理解錯了?

2009-12-20 16:14:01 補充:
I see. Hung Fung is wrong.


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