Sorry, no online dictionaries contain the exact phrase set of natural numbers.
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Reverse dictionary results:
1. integer
 2. sequence
3. real
4. distribution
5. mode
6. number
7. numbering
8. numbing
9. field
10. house
 11. conjugate
12. domain
13. binary code
14. uncountable
15. friendly
16. whole number
17. interval
18. average
19. continuum
20. addend
 21. combination
22. mean
23. means
24. countable
25. alphanumeric
26. array
27. card
28. cards
29. deviation
30. notation
 31. permutation
32. sequenced
33. sequencing
34. total
35. totaled
36. totalled
37. zero
38. lowest common multiple
39. characteristic
40. combination lock

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You can look up the words in the phrase individually using these links:   set ?   of ?   natural ?   numbers ?
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