"Axioms" Example Sentences
1. Axioms are the foundation of mathematical proofs.
2. The axioms of Euclidean geometry were first introduced by Euclid.
3. These axioms form the basis for our understanding of the physical world.
4. The axioms of set theory provide the framework for modern mathematics.
5. These axioms are intended to be self-evident and unprovable.
6. The axioms of logic are the rules by which we reason and make deductions.
7. These axioms are often taken for granted in everyday life.
8. The axioms of linear algebra are essential for understanding matrices.
9. These axioms are fundamental to the study of natural language.
10. The axioms of probability theory are used to make predictions about uncertain events.
11. These axioms can be used to derive a wide range of statistical methods.
12. The axioms of game theory describe the strategic behavior of rational agents.
13. These axioms explain why people often act in self-interest.
14. The axioms of quantum mechanics challenge our intuition about the physical world.
15. These axioms describe the behavior of particles at the atomic level.
16. The axioms of computer science are critical for developing algorithms and programs.
17. These axioms ensure correct and efficient computation.
18. The axioms of social choice theory deal with the aggregation of individual preferences.
19. These axioms help us understand how to make collective decisions.
20. The axioms of economics describe the behavior of consumers and producers.
21. These axioms provide the foundation for economic analysis and policy-making.
22. The axioms of ethics guide our moral reasoning and decision-making.
23. These axioms help us distinguish right from wrong.
24. The axioms of linguistics describe the structure and function of languages.
25. These axioms have practical applications in language teaching and translation.
26. The axioms of human rights provide the basis for laws and policies protecting individuals.
27. These axioms are essential for ensuring justice and equality in society.
28. The axioms of machine learning are used to create intelligent systems.
29. These axioms enable machines to learn from data and make predictions.
30. The axioms of biology describe the fundamental processes of life.
31. These axioms explain how organisms grow, reproduce, and adapt to their environment.
Common Phases
1. "According to the
axioms, we can deduce that..."
2. "Based on these
axioms, we can clearly see that..."
3. "The
axioms provide a solid foundation for understanding..."
4. "These
axioms form the fundamental principles underlying..."
5. "The
axioms serve as a starting point for deriving..."
6. "By accepting the
axioms, we can establish a consistent framework for..."
7. "The
axioms allow us to make logical inferences about..."
8. "Through the use of these
axioms, we can construct a rigorous proof of..."
9. "The validity of these
axioms is crucial for understanding..."
10. "By challenging the
axioms, we can push the boundaries of our knowledge in..."