The extended real numbers adjoin and to . They preserve the total order but leave some arithmetic expressions, such as , undefined.
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The extended real number line is a concept in mathematics that extends the usual set of real numbers to include two additional elements: positive infinity (\(+\infty\)) and negative infinity (\(-\infty\)). This extension is useful because it allows for a more comprehensive way to handle limits, summations, integrals, and other mathematical constructs.