| 31. | Thus the axiom of the empty set is implied by the nine axioms presented here.
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| 32. | Some authors include the empty set in this definition.
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| 33. | Zero is the supremum of the empty set and the infimum of " P ".
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| 34. | The empty set equipped with the empty binary operation satisfies this definition of a quasigroup.
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| 35. | Empty set cannot contain anything so it will not belong to our filter . 2.
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| 36. | The identity element is represented by the empty set.
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| 37. | In the empty set, we run a lot of routes to set up the run.
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| 38. | :What the OP is calling " nothing " is actually the " empty set ".
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| 39. | The Caratheodory extension gives all non-empty sets measure infinity.
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| 40. | Direct derivability is a relation between a sentence and a finite, possibly empty set of sentences.
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