"Hyperreals" Example Sentences
1. Hyperreals are a set of numbers that extend beyond the real numbers.
2. The concept of hyperreals was first introduced by Abraham Robinson.
3. Hyperreals are frequently used in non-standard analysis.
4. Infinitesimals are included in the set of hyperreals.
5. Hyperreals allow for the creation of infinitesimal and infinite numbers.
6. The set of hyperreals is uncountable.
7. Hyperreals can be used to solve problems in geometry and calculus.
8. Hyperreals are an example of a mathematical structure called a field.
9. Hyperreals include a vast range of numbers, including surreal numbers.
10. The addition of hyperreals is not commutative.
11. Hyperreals provide a way to model physical phenomena at extreme scales.
12. The usefulness of hyperreals in mathematical modeling is still being explored.
13. Hyperreals have applications in quantum mechanics.
14. The study of hyperreals is a branch of mathematical analysis.
15. The use of hyperreals can simplify some mathematical calculations.
16. The hyperreals are a non-standard real closed field.
17. Hyperreals are often used in the study of infinite games.
18. Addition and multiplication are both defined on hyperreals.
19. Hyperreals are used extensively in mathematical logic.
20. The order properties of the hyperreals differ from those of the reals.
21. Hyperreals can be used to model limit processes in calculus.
22. Hyperreals provide a way to bridge the gap between the finite and infinite.
23. Hyperreals can be used to study the behavior of functions near singularities.
24. The set of hyperreals is not algebraically closed.
25. Hyperreals can be used to study the behavior of sequences and series.
26. The axioms of hyperreals were first developed by Edwin Hewitt and Leonard Savage.
27. The existence of hyperreals was first proven by Abraham Robinson in the 1960s.
28. The use of hyperreals can simplify the study of differential equations.
29. Hyperreals are used in computer science to model non-standard data types.
30. The set of hyperreals can be used to construct a model of the universe.
Common Phases
Hyperreals are used to extend the real number system;
Hyperreals allow for infinitesimals and infinite numbers;
Hyperreals can be used to study limits and continuity in a more precise way;
Hyperreals have applications in calculus, number theory, and physics; The hyperreal number system is a non-standard model of calculus;
Hyperreals are an important tool in non-standard analysis.