"Bijections" Example Sentences
1. The set A and set B have bijections that can be defined as one-to-one correspondence.
2. The bijections between the set of odd numbers and the set of even numbers are not possible.
3. It's easy to find bijections between the set of reals and the set of irrationals because they are equinumerous.
4. A function can be a bijection if and only if it is both injective and surjective.
5. The group of bijections on a set X is called the symmetric group on X, denoted Sym(X).
6. The bijections between two finite sets of the same cardinality can be represented as permutation groups.
7. A bijection can be used to define a one-to-one correspondence between the elements of two sets.
8. The inverse of a bijection is also a bijection.
9. The bijections between the set of natural numbers and the set of prime numbers are infinite.
10. A function that is a bijection can be considered as a reversible transformation.
11. The number of bijections between a set A with n elements and itself is n!
12. The identity function is always a bijection.
13. The set of all bijections from a set X to itself forms a group under functional composition.
14. A finite set is equinumerous to any of its proper subsets if and only if there exists a bijection between them.
15. A bijection between two sets is a function that preserves both the order and the quantity of elements.
16. Two sets are said to be equinumerous if there exists a bijection between them.
17. A bijection between two sets ensures that every element in one set corresponds to exactly one element in the other set.
18. The bijections between the set of positive real numbers and the set of all real numbers are not possible.
19. A composition of two bijections is also a bijection.
20. A bijection is also known as a bijective function or a bijective mapping.
21. The inverse function of a bijection can be obtained by swapping the roles of the domain and the codomain.
22. The bijections between the set of natural numbers and the set of integers are infinite.
23. The bijections between a set A and a set B can be represented by a matrix.
24. The bijections between two infinite sets can be surprising and counterintuitive.
25. A set can have multiple bijections with itself, but they are all equivalent.
26. Stereographic projection is an example of a bijection between a sphere and a plane.
27. A bijection between two sets is a one-to-one and onto function.
28. The bijections between the set of positive integers and the set of even integers are not possible.
29. A bijection between two sets can be thought of as a matching between their elements.
30. The bijections between the set of rational numbers and the set of irrational numbers are not possible.
Common Phases
1. There exists a bijection between the sets A and B;
2. A bijection preserves the cardinality of a set;
3. Every finite set has a bijection to a segment of the natural numbers;
4. A bijection is a one-to-one and onto function;
5. Two sets have the same cardinality if and only if there exists a bijection between them;
6.
Bijections are useful for showing that two sets have the same size;
7. A composition of
bijections is also a bijection;
8. The inverse of a bijection is also a bijection;
9. The set of
bijections from A to B is denoted by B(A);
10. A permutation is a bijection from a set to itself.