When the left and right delimiter are the same symbol

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When the left and right delimiter are the same symbol, for example a vertical line, there can be more than one way of interpreting an expression with several sets of that delimiter.

For example, when a vertical line is used to represent the absolute value (or modulus) of a number, the following expression has at least two plausible interpretations, because Juxtaposition means combine in the obvious way

\[ |x|y|z| \]

If we write "the absolute value of $x$" as "$\operatorname{abs}(x)$", then the expression above could be interpreted as:

  • $\operatorname{abs}(x) \cdot y \cdot \operatorname{abs}(z)$
  • $\operatorname{abs}(x \cdot \operatorname{abs}(y) \cdot z)$