Symbolic Overload Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
What does the symbol ∣| mean in ∣x∣|x| vs in {x∣x>0}\{x \mid x > 0\}?

Solution

  1. 1
    In ∣x∣|x|: absolute value (distance from zero).
  2. 2
    In {x∣x>0}\{x \mid x > 0\}: 'such that' (set-builder notation).

Answer

Absolute value vs 'such that'.
The vertical bar is one of the most overloaded symbols in math. It can mean absolute value, 'divides' (a∣ba | b), 'such that', determinant, or 'evaluated at'. Context is everything.

About Symbolic Overload

The situation where the same symbol carries different mathematical meanings depending on the context it appears in.

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More Symbolic Overload Examples

Example 1 medium

List three different meanings of the symbol [formula] in mathematics.

Example 2 hard

What does [formula] mean in each context: (a) [formula], (b) [formula], (c) 'the function [formula]'

Example 4 medium

In [formula] and [formula], the superscript means different things in context. Explain.

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