# how do I find a undecidable subset of a set that's decidable? [closed]

Given that Let S = {a | |a| is odd}. I know that since S is decidable, but does there exist a subset within S that is undecidable?

## closed as unclear what you're asking by D.W.♦, FrankW, Juho, David Richerby, vonbrandMar 21 '14 at 0:04

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• This is a dump of a homework problem. It has also been previously asked on this site. – Yuval Filmus Mar 20 '14 at 1:57
• Any set (even undecidable ones) are subsets of the set of all strings... – vonbrand Mar 21 '14 at 0:04

Hint: For every language $L$, the language $M = \{ 1^{2x+1} : x \in L \}$ is a subset of $S$.
• Here $1^{2x+1}$ is the string of length $2x+1$ consisting only of $1$s. – Yuval Filmus Mar 20 '14 at 2:05
• Well, $S$ consists of all strings of odd length... – Yuval Filmus Mar 20 '14 at 2:15