$A=\{7,14,21,28\}$ is the set-builder notation $\{x \in \mathbb N:x=7n, n \in \mathbb N \text{ and } 1\le n \le 4\}$ right?

  • $\begingroup$ A={7,14,21,28} (it's not a sequence). It looks correct to me. I would probably use $\land$ instead of comma or descriptive text ("and") though. Not sure if it is necessary with things like $\forall$ etc, guess it depends on the formality level. $\endgroup$
    – Emil
    Feb 19, 2016 at 9:41
  • $\begingroup$ Wellcome to MSE !! $\endgroup$
    – HK Lee
    Feb 19, 2016 at 9:45
  • $\begingroup$ It is indeed correct but it does carry some redundancies (you've said that $n \in \mathbb{N}$, which already means that $x=7n \in \mathbb{N}$, so saying prior to that that $x \in \mathbb{N}$ is unnecessary). $\endgroup$ Feb 19, 2016 at 10:14

1 Answer 1


Yes, it is correct.

See also The following questions with answers, where more set builder notation very similar examples are discussed: This, This and Especially This.


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