Set theory

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Across
  1. 4. The first of the transfinite cardinal numbers.
  2. 5. is the unique set having no elements
  3. 7. the set theory symbol for the smallest infinite set larger than. (Aleph-0), which in turn is equal to the cardinal number of the set of countable ordinal numbers.
  4. 9. the set of all ordered pairs (x, y) such that x belongs to A and y belongs to B.
  5. 11. includes the set of real numbers ® and the set of pure imaginary numbers.
  6. 12. those elements in A or B, but not in both A and B.
  7. 13. A set that contains all the subsets of a given set along with the empty set
  8. 14. a set of elements in the universal set that is not part of the original set
  9. 15. When a point, object, or number does not belong to a specified set
Down
  1. 1. the number of elements in a given mathematical set.
  2. 2. is used in mathematical set theory to indicate that a point, object, or number belongs to a certain set
  3. 3. a pair of objects
  4. 6. the set of elements contained in a given set that are not elements of another specified set.
  5. 8. the union of the set of rational numbers (Q) and the set of irrational numbers
  6. 10. is a set which contains all objects, including itself