0
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$$\{n | n \in \mathbb N \text{ and } n\cdot n + n \text{ is a multiple of } 5 \text { and } n \leq 12\}$$

I put $\{4,5,9,10\}$ but apparently this is still a proper set not the complete answer?

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    Is, according to your definitions, $0 \in N$?2012-04-23
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    Depends on whether your math teacher considers $0$ a natural number, but most set theory books do.2012-04-23
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    Also what was the edit?2012-04-23
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    I edited for formatting (you had $<=$ for example. Just tweaks to the format. You can click on the "Edited..." text to get a diff of the edit.2012-04-23
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    I don't think there's any reason to be profane in the comments, even if the teacher is not behaving ideally...2012-04-23
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    @JamieB: Because then she would deprive you of the exercise of *figuring out for yourself* that you were missing 0. Remember, the point of an exercise is usually not to get the solution, but to learn *how to solve problems*. You don't get any problem solving experience if you're simply *told* what you did wrong, rather than working it out for yourself.2012-04-23
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    I guess it's one of these 'You'd have to see to understand'. Also for the others, I don't consider my comment profane, maybe culture clash there, swearing would be much worse than that :)2012-04-23
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    Math teachers may consider 0 a natural number, but number theorists know that it isn't.2012-04-24
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    I actually prefer the notation that I've heard Peano himself used: $\mathbb N$ for the natural numbers *without* $0$, and $\mathbb N_0$ for the natural numbers *with* $0$.2012-08-21
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    @Gerry: And set theorists know that number theorists are just wrong... :-)2012-10-26
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    @Asaf, Rule #1: Number theorists are always right. Rule #2: If a number theorist is wrong, see Rule #1.2012-10-27
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    @Gerry: Rule #1 implies a contradiction; therefore Rule #2 is consistent relative to it.2012-10-27

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