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The Time War , more specifically called the Last Great Time War , [2] [3] is a conflict within the fictional universe of the British science fiction television series Doctor Who. The conflict pitted the Time Lords against the Daleks and culminated in the apparent mutual destruction of both races, caused by the Doctor. In the Doctor Who continuity, the war occurs between the events of the film and the revived series. It was frequently mentioned and alluded to from the first series of the show's return, [4] [5] but was not directly seen until the show's 50th anniversary special. Short comments in various episodes act as hints, but the war was not explicitly discussed until the episode " The Sound of Drums "; [6] part two of the two-part special " The End of Time " — [7] provided further information and revealed the Time Lord leaders' sinister endgame.

In combinatorics , a branch of mathematics , the inclusion—exclusion principle is a counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets ; symbolically expressed as. The formula expresses the fact that the sum of the sizes of the two sets may be too large since some elements may be counted twice. The double-counted elements are those in the intersection of the two sets and the count is corrected by subtracting the size of the intersection.

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