# Set notation for infinite subsets.

In set notation, how can one express an infinite set of subsets where each subset has exactly two elements $\{an-1, an+1\}$ where $a$ is a constant and $n\ge1$ and the $n$ value for each subset is one more than that of the previous subset. Example: $\{ \{a1-1, a1+1\},~\{a2-1, a2+1\},~\{a3-1, a3+1\},~. . . \}$

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## 1 Answer

What about $\{\{an-1, an+1\}\ |\ n \in \mathbb{N}\setminus\{0\}\}$? Alternatively, for $n \in \mathbb{N}\setminus\{0\}$ you could define $A_n = \{an-1, an+1\}$ and the set you're interested in is $\{A_n\ |\ n \in \mathbb{N}\setminus\{0\}\}$.

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Thanks, what about the part about $n$ for each subset being one more than the $n$ value for the previous subset? – Babiker Jan 21 at 6:28
A set has no order, so there is no sense of the previous subset. I've edited my answer so that it is clear that $n$ is a positive integer. Does that answer your question? – Michael Albanese Jan 21 at 6:40
Yes, thanks you. – Babiker Jan 21 at 6:45
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