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For set theory, we have notation to denote subsets, e.g.: $$S \subset X$$

When working with expressions (arithmetic, Boolean, etc.), is there a notation to denote expression $S$ is a valid sub-expression of $X$?

For instance, if we have $X := 5 \times (3+4)$, then we can say $5$, $3+4$, and $(3+4)$ are valid sub-expression of $X$, but $5 \times$ is not since it cannot be correctly evaluated, and neither is $2+3$ a valid sub-expression of $X$, since, well, obviously it isn't.

If there is no convenient notation, what is a clear way to word it (apparently "sub-expression" is not desirable to some)?

bbarker
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    The word "subexpression" is commonly used. I suggest that you pick some symbol like $\prec$ or $\lhd$ that resembles a less-than sign and say up front something like "We will write $a\lhd b$ to mean that $a$ is a subexpression of $b$; for example $5\lhd 5\times(3+4)$ and $3+4\lhd5\times(3+4)$." This too is common. – MJD Jul 17 '14 at 23:27
  • From other options there is $\sqsubset$. Also note that there are „strict“ and „non-strict“ variant for each symbol. E.g. for subset symbol, $⊆$ is non-strict, $⊊$ is strict and $⊂$ is either strict or non-strict debending on your convention. – Adam Bartoš Jul 19 '14 at 18:42

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