Purchase Solution

Cardinality, countability

Not what you're looking for?

Ask Custom Question

2-12 through 2-14.

Exercise 2-12. Consider the integers in the arrangement 0, 1, -1, 2, -2, 3, -3, ... Let n E N. Which integer occupies the 2n position? The 2n+ 1 position? Prove that I and N can be put into one-to-one correspondence.

From Exercise 2-12, I has N0 integers. As we have seen, adding one new members to a countable infinity does not change the cardinal number of a set.

Exercise 2-12. Prove that adding a finite number n of new members to a countably infinite set does not change its cardinal numbers. (Find a one-to-one correspondence as in the hotel illustration proceeding Definition 2-10.)
2-12, Not sure what they are asking with position of 2n, 2n+1 position of the integers. The third part, proof on how to get the integers and N into one to one, can I just show ordering hence; 1,2,3,4, ... and 0,1,-1,2,-2,... or should there be more

Exercise 2-14. Prove that n countably infinite sets can be put into one-to-one correspondence with one countably infinite set. (Use the technique of Exercise 2-12.)

Purchase this Solution

Solution Summary

This solution answers various questions regarding cardinality and countability.

Solution Preview

See the attachment.

Ex. 2-12. The number n occupies the 2n position, and the number (-n) occupies the (2n+1) position.
The given arrangement gives a one-to-one correspondence. Indeed, different integers are located into different positions. Moreover, any position contains some integer.
Ex.2-13. Let identify the elements of a countably infinite set with ...

Purchase this Solution

Free BrainMass Quizzes
Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

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

Multiplying Complex Numbers

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

Exponential Expressions

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