Hilton Hall
04/25/2023 · Middle School
\( \forall \epsilon>0 \quad|\cos (m)| \leqslant \epsilon \) isit correct?
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The statement provided is a mathematical inequality involving the cosine function. The statement claims that for all positive values of \( \epsilon \), the absolute value of the cosine of \( m \) is less than or equal to \( \epsilon \).
To determine if this statement is correct, we need to consider the properties of the cosine function. The cosine function has a range of \([-1, 1]\), which means that the absolute value of the cosine of any angle is always less than or equal to 1.
Therefore, the statement \( \forall \epsilon>0 \quad|\cos (m)| \leqslant \epsilon \) is correct because the absolute value of the cosine of any angle is always less than or equal to 1, which is less than or equal to any positive value of \( \epsilon \).
Quick Answer
The statement is correct because the absolute value of the cosine of any angle is always less than or equal to 1, which is less than or equal to any positive \( \epsilon \).
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