Sorry, no online dictionaries contain the exact phrase extended real number.
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Reverse dictionary results:
1. multiplication
 2. irrational
3. magnitude
4. irrational number
5. administrator
6. degree
7. amplitude
8. absolute
9. modulus
10. scalar
 11. transcendental
12. complex
13. complex conjugate
14. continuum
15. convergent
16. decimal
17. brake
18. mora
19. his
20. imaginary
 21. absolute value
22. rational number
23. algebraic number
24. dot product
25. inner product
26. scalar product
27. complex number
28. complex quantity
29. imaginary number
30. indefinite integral
 31. nies
32. positional notation
33. metric
34. positional representation system
35. great
36. large
37. long
38. reach
39. reaches
40. reaching

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You can look up the words in the phrase individually using these links:   extended ?   real ?   number ?
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