Counting discontinuities of a function

Supposing that is a function defined on an interval we will denote by the set of all discontinuities of on By we will mean the set of all such that has a removable discontinuity at Analogously by we denote the set constituted by all such that has a jump discontinuity at The set of all such that has an essential discontinuity at will be denoted by Of course then

The two following properties

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