Exercise · ZW-CONSTRUCTION-OF-THE-NATURALS-001 · ★☆☆ Basic
What is the set \(1\) in the von Neumann construction?
Choose one option.
Show answer
- B. \(\{0\}\)
Explanation
With \(0=\varnothing\), the successor \(0^+=0\cup\{0\}\) gives \(\{0\}\).
Review the concept: Construction of the naturals
The natural numbers are a set \(\mathbb{N}\) built inside set theory as finite ordinals, where each natural is the set of all naturals smaller than it.
\[n^+ = n \cup \{n\}\]
More practice problems: construction of the naturals
- ZW-CONSTRUCTION-OF-THE-NATURALS-002 What set is 0 in this construction?
- ZW-CONSTRUCTION-OF-THE-NATURALS-003 How many elements does the natural 4 have?
- ZW-CONSTRUCTION-OF-THE-NATURALS-004 What is the successor of 2?
- ZW-CONSTRUCTION-OF-THE-NATURALS-005 Compute 2^+ using the definition of successor.
- ZW-CONSTRUCTION-OF-THE-NATURALS-006 How many elements does 3^+ have?
- ZW-CONSTRUCTION-OF-THE-NATURALS-007 If n=\0,1\, what is n^+?
- ZW-CONSTRUCTION-OF-THE-NATURALS-008 What is the set ℕ∩\0,1,2\ of naturals less than 3?
- ZW-CONSTRUCTION-OF-THE-NATURALS-009 Let A=\x∈ℕ: xne 0\. Which statement correctly shows that A is not inductive?