EDB β€” 0B3

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Definition 15

[0B3] Let IβŠ†β„ be a set, x0βˆˆβ„β€• an accumulation point for I. Let P(x) be a logical proposition that we can evaluate for x∈I. We define that

”P(x) holds eventually for x tending to x0” if

there is a neighborhood U of x0 βˆ€x∈U∩I, P(x) is true  ;

”P(x) frequently holds for x tending to x0” if

for every neighborhood U of x0 βˆƒx∈U∩I for which P(x)  ;


where it is meant that the neighbourhoods are ”deleted”.

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  • accumulation point, in the real line
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