Countable/Uncountable Sets
Not what you're looking for?
Please see the attached image for questions I and II.
III) If A is a countable subset of an uncountable set X, prove that X A is uncountable.
IV) Suppose that f is a function from X into Y so that the range of f is uncountable. Prove that X is uncountable.
V) Prove that the set of all polynomials with rational coefficients is countable.
VI) A real number a is said to be an algebraic number if there exists a polynomial p(x) with integer coefficients such that p(a) = 0. Prove that the set of algebraic numbers is countable. (Hint: use V))
Purchase this Solution
Solution Summary
Countable/Uncountable Sets are clarified.
Purchase this Solution
Free BrainMass Quizzes
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.
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.