Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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: $\{ \{a1-1, a1+1\},~\{a2-1, a2+1\},~\{a3-1, a3+1\},~. . . \}$

share|improve this question
add comment

1 Answer 1

up vote 1 down vote accepted

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 $\{A_n\ |\ n \in \mathbb{N}\setminus\{0\}\}$.

share|improve this answer
    
Thanks, what about the part about $n$ for each subset being one more than the $n$ value for the previous subset? –  Babiker Jan 21 '13 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 '13 at 6:40
    
Yes, thanks you. –  Babiker Jan 21 '13 at 6:45
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.