Q4 (10 points) Prove that \( \mathbb{N} \times \mathbb{Q} \) is a countable set.
Added by Kelsey W.
Close
Step 1
A set is countable if it is finite or if it has the same cardinality as the set of natural numbers, \( \mathbb{N} \). The set \( \mathbb{N} \) represents the set of natural numbers, and \( \mathbb{Q} \) represents the set of rational numbers. Show more…
Show all steps
Your feedback will help us improve your experience
Maujee Lal and 53 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Show that the set $\mathbf{Z}^{+} \times \mathbf{Z}^{+}$ is countable.
Basic Structures: Sets, Functions, Sequences, Sums,and Matrices
Cardinality of Sets
Show that the set {ጥ/m + ጥ/n : m, n ∈ N} is countable.
Adi S.
Prove that every subset of a countable set is countable.
Recommended Textbooks
Elementary and Intermediate Algebra
Algebra and Trigonometry
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD