Is {x/(x+1) : x∈ℕ} a subset of ℚ? Which sets are uncountable?

[KOO]

Question 1) Write ⊆ or ⊄:

{x/(x+1) : x∈N} ________ QNOTE:
⊆ means SUBSET
⊄ means NOT A SUBSET
∈ means ELEMENT
N means Natural Numbers
Q means Rational Numbers

Question 2)
Which of the following sets are infinite and uncountable?
R - Q
{n∈N: gcd(n,15) = 3}
(-2,2)
N*N
{1,2,9,16,...} i.e the set of perfect squares

 

[topsquark]

Question 1) Write ⊆ or ⊄:

{x/(x+1) : x∈N} ________ QNOTE:
⊆ means SUBSET
⊄ means NOT A SUBSET
∈ means ELEMENT
N means Natural Numbers
Q means Rational Numbers

Question 2)
Which of the following sets are infinite and uncountable?
R - Q
{n∈N: gcd(n,15) = 3}
(-2,2)
N*N
{1,2,9,16,...} i.e the set of perfect squares

1) Is x/(x + 1), when x is a natural number, a rational number?

2) Is R countable? Is Q countable?

-Dan