Purchase Solution

# Cardinality, countability

Not what you're looking for?

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.)

##### 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 ...

##### 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.