- #1
jackbauer
- 10
- 0
Hi people, I need some help with these questions please:
1.Is the set of all x in the real numbers such that (x+pi) is
rational, countable?
I don't think this is countable, isn't the only possible value for x = -pi, all other irrationals will not make x+pi rational i thought?
2.Is the set of all x in the real numbers, such that for all k, (x+the square root of k) is not a natural number, countable?
Again I don't think this is countable because if the square root of k is irrational, like it is for k=2, then you can add infinitely many values of x to root k for which the sum of x and root k is not natural.
Lastly, is every infinite subset of the power set of the naturals uncountable?
I don't think so because P(N), the power set of N, has cardinality 2^(aleph nought) and is countable, hence it's subsets will be countable.
Could anyone offer some advice,
Cheers,
JB
1.Is the set of all x in the real numbers such that (x+pi) is
rational, countable?
I don't think this is countable, isn't the only possible value for x = -pi, all other irrationals will not make x+pi rational i thought?
2.Is the set of all x in the real numbers, such that for all k, (x+the square root of k) is not a natural number, countable?
Again I don't think this is countable because if the square root of k is irrational, like it is for k=2, then you can add infinitely many values of x to root k for which the sum of x and root k is not natural.
Lastly, is every infinite subset of the power set of the naturals uncountable?
I don't think so because P(N), the power set of N, has cardinality 2^(aleph nought) and is countable, hence it's subsets will be countable.
Could anyone offer some advice,
Cheers,
JB