Notation Overload Math Example 3

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Example 3

easy
The symbol ∣⋅∣|\cdot| is used for absolute value of numbers and cardinality of sets. Evaluate: (a) ∣−3∣|-3|, (b) ∣{1,2,3}∣|\{1,2,3\}|.

Solution

  1. 1
    (a) Absolute value: ∣−3∣=3|-3| = 3.
  2. 2
    (b) Cardinality: ∣{1,2,3}∣=3|\{1,2,3\}| = 3 (three elements).

Answer

(a)  3,(b)  3(a)\;3,\quad (b)\;3
The vertical bar notation ∣⋅∣|\cdot| is overloaded: for numbers it means distance from zero (absolute value); for sets it means number of elements (cardinality). The type of the argument reveals the intended meaning.

About Notation Overload

When the same symbol is used to mean different things in different contexts, requiring the reader to infer meaning from context.

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More Notation Overload Examples

Example 1 easy

The symbol [formula] is used in three different ways in mathematics. Identify each usage and give an

Example 2 medium

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Example 4 medium

The letter [formula] can represent: Euler's number [formula], an element of a set, or a vector. In t

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