Definition:Continuous Real Function/Half Open Interval

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Definition

Let $f$ be a real function defined on a half open interval $\left({a \,.\,.\, b}\right]$.

Then $f$ is continuous on $\left({a \,.\,.\, b}\right]$ if and only if it is:

$(1): \quad$ continuous at every point of $\left({a \,.\,.\, b}\right)$
$(2): \quad$ continuous on the left at $b$.


Let $f$ be a real function defined on a half open interval $\left[{a \,.\,.\, b}\right)$.

Then $f$ is continuous on $\left[{a \,.\,.\, b}\right)$ if and only if it is:

$(1): \quad$ continuous at every point of $\left({a \,.\,.\, b}\right)$
$(2): \quad$ continuous on the right at $a$.


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