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These problems deal with sequences of numbers. Can you spot what the sequences' rules are?

Design a sequence S_{0} , S_{1} , ... , S_{∞} where each S_{i}
1) is a string of characters from the set
{φ, "right brace", "left brace", comma} (φ denotes the empty set),
2) denotes a valid set, and
3) |S_{i} | = i.
For clarity you can define substrings and use recursion.
Note; S_{i} = {φ,{φ},{φ},φ,{φ,{φ}}} = {φ,{φ},{φ,{φ}}}
|S_{i} | = 3 not |S_{i} | = 5.
Note: φ = {}. I don't know if this will
help.
A possible start: S_{0} = φ , S_{1} = {φ} , ...

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