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Excluding

/ɪkˈskluːdɪŋ/preposition / verb
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Excluding means to leave out or not include something from a group, set, or consideration, often to specify an exception clearly. In modern contexts, it's widely used in legal, scientific, and everyday language to define boundaries and prevent misunderstandings, making it essential for precise communication.

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The principle of exclusion underpins the inclusion-exclusion theorem in mathematics, which was formalized by Abraham de Moivre in 1718 and helps calculate probabilities in overlapping sets; for instance, it can determine the exact number of elements in a union of three sets as |A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|.

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