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Given the set builder notation $S = \{n \in \mathbb{N} \ | \ n \text{ is even}\}$, what does $S$ look like?

Does $S = \{0, 2, 4, 6, 8, 10, 12, ...\}$? Or am I missing something?

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Unfortunately, there is no consensus in Mathematics about if $0 \in \Bbb N$ or not. So, depending on the context or the area you are working, $0$ could be not included. Apart from that, you are right.

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