Purchase Solution

Functions and Same Cardinality

Not what you're looking for?

Ask Custom Question

Find a function that is one-to-one to show the following sets have the same cardinality. Let N=(1,2,3,4,5,6,7,8,9,...)

N and A= (2n l n E N)

Purchase this Solution
Solution Summary

Cardinality is investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

Solution Preview

Please see the attached file for the complete solution.
Thanks for using BrainMass.

Let and
Define the function as ...

Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Probability Quiz

Some questions on probability

View More Free Quizzes
Related BrainMass Solutions

  • Question about group theory, cardinality and isomorphic

    Z- integer To prove that two sets A & B have the same cardinality, we prove that there is a bijection (a one-to-one and onto map) from A to B.

  • Sets Definitions and Examples

    However, equal sets are sets which have both the same number of elements, and the exact same entries. For example, the sets {2, 4, 6} and {1, 3, 5} are equivalent sets but not equal sets.

  • Real Analysis : Lebesgue Measure

    And the range of h is atmost the cardinality of f(A)Xg(B). Hence h is a simple function. Similarly, the product function defined by is also measurable as f,g are measurable. And the range of k is atmost the cardinality of f(A)Xg(B).

  • Prove same cardinality

    24212 Prove same cardinality Prove that Rsquared has the same cardinality of R (hint: think of shuffling two string of digits) See attachment for full question Please see attached file

  • Cardinality of R and R^2

    A proof that R and R^2 have the same cardinality.

  • Kernel equivalence and natural mapping

    Thus elements of the same equivalence class map to the same element of %(A), and elements of different equivalence classes map to different elements of %(A).

  • Uncountable Basis

    And as the cardinality must be |R|, we have that |B| = |R|. Uncountability of a basis is investigated.

  • Providing proof about Cardinality

    But , as we already proved, the sets (A^B)^C and A^(BxC) are bijective, and hence have the same cardinalities. Thus, we conclude that numbers (a^b)^c and a^(bxc) are equal.

  • The common notion 5 "The whole is greater than the part"

    But the cardinality of E and O is the same as the cardinality of N. The cardinalities of infinite sets are called transfinite numbers.

View More Related Solutions