"Commutative" Example Sentences
1. The commutative property of addition states that changing the order of the addends does not change the sum.
2. The commutative property of multiplication states that changing the order of the factors does not change the product.
3. Algebraic equations involving commutative operations are easier to solve.
4. Addition and multiplication are the two most common commutative operations.
5. The commutative diagram is an important tool in category theory.
6. The commutative law of logic states that the order of propositions and their connectives do not matter as long as the truth values are preserved.
7. The commutative property of sets states that the order of elements in a set does not matter.
8. The commutative ring is a fundamental concept in abstract algebra.
9. The commutative property of matrices applies only to square matrices.
10. Modular arithmetic is an example of a commutative operation.
11. The commutative property of functions states that the order of composition does not matter.
12. The commutative property of limits states that the order of taking limits does not matter.
13. The commutative law of vector addition states that changing the order of vectors does not change the result.
14. Commutative diagrams are widely used in geometry and topology.
15. The commutative group is a special type of group in abstract algebra.
16. Commutative diagrams simplify proofs in category theory.
17. Commutative rings are studied in number theory and algebraic geometry.
18. The commutative property of conjugation states that reversing the order of multiplication does not change the result.
19. The commutative property of cross product in vector calculus states that changing the order of vectors only affects the sign of the result.
20. The commutative law of addition applies to complex numbers.
21. The commutative property of scalar multiplication in linear algebra states that the order of multiplication does not matter.
22. The commutative property of tensor product in abstract algebra states that changing the order of factors only affects the sign of the result.
23. Commutative semigroups are a subfield of algebraic structures.
24. The commutative law of multiplication applies to quaternions.
25. Commutative diagrams in topology help visualize the relationships between spaces and maps.
26. The commutative law of exponentiation states that changing the order of exponentiation does not change the result.
27. The commutative property of dot product in vector calculus states that changing the order of vectors does not change the result.
28. Commutative categories are a key concept in higher category theory.
29. The commutative law of implication in propositional logic states that exchanging antecedent and consequent does not change the implication.
30. Commutative algebras are studied in many fields of mathematics, including physics, computer science, and engineering.
Common Phases
1. The
commutative property states that the order of the terms in a mathematical operation can be switched without affecting the final result;
2. Addition and multiplication are both
commutative operations;
3. The
commutative property is an essential concept in abstract algebra;
4. The
commutative property is not always true for other mathematical operations such as subtraction or division;
5. The
commutative property is one of the most basic properties of arithmetic;
6. The
commutative property can be used to simplify algebraic expressions;
7. The
commutative property is a type of symmetry in mathematics;
8. The
commutative property is often taught in elementary school math classes.