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A sequence X is define as numbers smaller than 10 that are divisible by 2 and a natural number. What are the domain and ranges?

I assume that the domain and range here is:

dom X = <1,2,3,4,5,6,7,8,9> ran X = <2,4,6,8> 

I'm not sure if this is correct, can anyone verify? Especially the dom X part, i'm not sure about that.

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The question cannot be answered without further information. If I understand the question correctly, the range of the sequence is either $\{0,2,4,6,8\}$ or $\{2,4,6,8\}$, depending on whether your definition of natural number includes $0$; mine does, but yours may not. However, there is no way to tell what the domain is unless your textbook or instructor has established some convention. If the sequence is one-to-one, listing each number in the range only once, the two most likely conventions would make the domain either $\{0,1,2,3,4\}$ or $\{1,2,3,4,5\}$ if the range is $\{0,2,4,6,8\}$, and $\{0,1,2,3\}$ or $\{1,2,3,4\}$ if the range is $\{2,4,6,8\}$.

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    @Mark: No, I said that it’s one of the two likeliest conventions; since you don’t include $0$ among the natural numbers, I’d now say that it’s *the* likeliest. But as I said, there’s no way for me to know for sure what domain is intended. There is nothing to prevent the domain of a $4$-term sequence from being $\{-2,-1,0,1\}$, for instance, or $\{3,6,9,12\}$, among many other possibilities. What answer is intended depends on the assumptions made by your text or your instructor, but in general $\{1,2,\dots,n\}$ is the most common domain for an $n$-term sequence if $0$ isn’t considered natural.2012-09-20