Real Analysis Crossword

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Across
  1. 1. a type of convergence for a sequence of functions
  2. 4. the limit of the supremums in a sequence
  3. 6. a differentiable function has one
  4. 9. the partial sums of a sequence of positive terms
  5. 14. the part of a theorem that is proved
  6. 18. the name of the mathematician who showed that derivatives satisfy the intermediate value property irrespective of their continuity
  7. 19. one of the standard notation for an arbitrary small number
  8. 21. a type of sequence that is equivalent to a convergent sequence
  9. 24. a property of the rational numbers in the real numbers
  10. 25. the greatest lower bound
  11. 28. a type of continuity and a type of convergence
  12. 32. a type of sequence without a limit
  13. 34. increasing or decreasing
  14. 35. an immediate consequence of a theorem
  15. 36. a set that contains all its limit points
  16. 37. the study of open and closed sets
  17. 40. a function where the inverse image of any open set is open
  18. 42. the real numbers are formed as the completion of this type of number
  19. 44. a type of sequence that has a limit
  20. 45. the least upper bound
Down
  1. 2. a sequence within a sequence
  2. 3. a type of continuity that differentiable functions must satisfy at least locally
  3. 5. a convergent sequence has a unique one
  4. 7. a statement assumed to be true
  5. 8. an open interval
  6. 10. a type of proof where the conclusion is negated
  7. 11. course covering the rigorous proof of statements in calculus
  8. 12. a type of convergence for infinite series where rearrangements do not affect the sum
  9. 13. a set that is closed and bounded
  10. 15. a set of numbers that be added and multiplied that satisfy certain axioms (reals, rationals and complex numbers are some examples)
  11. 16. a division of an interval into a finite set of numbers
  12. 17. a set that is not finite or in one-to-one correspondence with the natural numbers
  13. 18. a place with continuity fails
  14. 20. a list of elements that is in one-to-one correspondence with the natural numbers
  15. 22. the limit of the infimums in a sequence
  16. 23. a set with no elements
  17. 26. a type of number that is not rational
  18. 27. one of the standard notations for an arbitrary small number
  19. 29. bounded continuous functions and bounded monotone functions are examples of these types of functions
  20. 30. a set that contains a neighborhood of each point
  21. 31. the part of a theorem defining the assumptions
  22. 33. a statement that can be proved
  23. 38. why we know a statement is true in this course
  24. 39. a property of the real numbers not shared by the rational numbers
  25. 41. every bounded monotonic set of a real numbers must do this
  26. 43. a set that can not be covered by two disjoint open sets