Q BgQuestion:

Scholar
Karma Points: 200
Respect (41%):
posted by  Probability (7th) on 8/26/2008 9:06:36 AM  |  status: Live  

real analysis by frank morgan

Course Textbook Chapter Problem
Other real analysis by frank morgan 1 1,2,3,4,5
Question Details:
exercise 2.
 
1)prove whether or not the set S is countable.
a) S = { irrational }
b) S = { terminating decimals }
c) S = [0, .001)
d) S = Q X Q
e) S = R X Z
 
 
2) prove that the  intersection  of two countable sets is countable.
 
3) prove whether or not the intersection and union  of two uncountable sets must be uncountable.
 
4) prove that the cartesian product of two countable sets      AX B = { (a,b): aεA and bεB) }
 
5) prove that a countable union of countable sets is countable.
 
reply soon.
Tags: Math, Other
Bonus Point Alert! Earn +2 additional karma points for helping this monthly member.

AAnswers:

Answer Question
(Cramster SME)
posted by Galois on 8/29/2008 12:50:39 AM  |  status: Live
Asker's Rating: This answer has not been rated. If you asked this question, then please login.   
Response Details:
a)Countable
b)Countable
c)Uncountable
d)Countable
e)Uncountable
2)Let A and B are any two countable sets.
and we know AB is subset of A and B, and we have every subset of countable set is countable.
∴ AB is countable.
3)Let A and B are two uncountable sets,AB.
Suppose AB is countable, then both A and B has to be countable, but by hypothesis A and B are uncountable. ∴AB is uncountable.
 
Tags: Math, Other
Answer Question
Ask New Question

Join Cramster's Community

Cramster.com brings together students, educators and subject enthusiasts in an online study community. With around-the-clock expert help and a community of over 100,000 knowledgeable members, you can find the help you need, whenever you need it. Join for free today » How Cramster is different than tutoring »