MHB Natural Numbers ⊆/⊄ Rationals: Infinite & Uncountable Sets

AI Thread Summary
The discussion centers around the relationship between natural numbers and rational numbers, specifically whether the set {x/(x+1) : x∈N} is a subset of Q. Participants are asked to determine if this set is a subset (⊆) or not (⊄) of rational numbers. Additionally, the conversation explores which sets are infinite and uncountable, including the set of real numbers minus rational numbers (R - Q) and the Cartesian product of natural numbers (N*N). The participants also discuss the countability of the real numbers (R) and rational numbers (Q). The thread highlights key concepts in set theory and the nature of different number sets.
KOO
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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
 
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KOO said:
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
 
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