One-Sided Limit of Real Function/Examples/Floor of 1 minus Size x
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Example of One-Sided Limit of Real Functions
Let $f: \R \to \R$ be the real function defined as:
- $\map f x = \floor {1 - \size x}$
Then:
- $\ds \lim_{x \mathop \to 0} \map f x = 0$
but:
- $\map f 0 = 1$
Sources
- 1961: David V. Widder: Advanced Calculus (2nd ed.) ... (previous) ... (next): $1$ Partial Differentiation: $\S 2$. Functions of One Variable: Exercise $2$