Practice Notation Overload in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

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

The same word meaning different things in different conversations — context tells you which meaning applies, but this can trip up a reader who is new to the context.

Example 1

easy
The symbol - is used in three different ways in mathematics. Identify each usage and give an example.

Example 2

medium
The notation (a, b) is used for an ordered pair, an open interval, and the GCD. For each usage, write an example sentence and state how context disambiguates.

Example 3

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

Example 4

medium
The letter e can represent: Euler's number \approx 2.718, an element of a set, or a vector. In the expression \ln(e^2), which meaning applies, and what is the value?
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