ECON 2P30 Lecture Notes - Open Set, Infimum And Supremum, Compact Space

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With the de nition of a function, we are often concerned with the function value as the variable concerned approaches arbitrarily close to a certain point. Hence, we use the notion of limits to address this issue. For example, when we write: lim x z f (x) (1) this is to denote the function value of the function f (x) as x approaches: similarly, we can write this limit in alternative ways. For example, limx z f (x) = lim 0 f (z + ). When the limit of a function f (x) as x approaches some value z is say y, we write limx z f (x) = y. In fact, we are always talking about the value of f (x) when x approaches z. In this sense, even if the function f (x) is not de ned when x = z the limit as x approaches z may still exist.

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