Exercise · ZW-EQUIPOTENCE-003 · ★☆☆ Basic
Which of these properties does equipotence satisfy?
Choose one option.
Show answer
- C. It is reflexive, symmetric and transitive
Explanation
Every set is equipotent to itself via the identity, and the inverse and composition of bijections are bijections. It is not antisymmetric: \(\mathbb{N}\sim\{0,2,4,\dots\}\) but \(\mathbb{N}\neq\{0,2,4,\dots\}\).
Review the concept: Equipotence
Two sets \(A\) and \(B\) are equipotent if there is a bijection \(f\colon A\to B\). It is written \(A\sim B\).
\[A\sim B \iff \exists\, f\colon A\to B\ \text{biyectiva}\]
More practice problems: equipotence
- ZW-EQUIPOTENCE-001 What is needed for two sets A and B to be equipotent?
- ZW-EQUIPOTENCE-002 Is \a,b,c\ equipotent to \1,2,3\?
- ZW-EQUIPOTENCE-004 Let ℕ=\0,1,2,dots\. Is ℕ equipotent to \0,2,4,dots\?
- ZW-EQUIPOTENCE-005 Which statement about ℕ and ℤ is correct?
- ZW-EQUIPOTENCE-006 How is it written that the sets A and B are equipotent?
- ZW-EQUIPOTENCE-007 Is \1,2\ equipotent to \1,2,3\?
- ZW-EQUIPOTENCE-008 What do you get when composing two bijections fcolon A→ B and gcolon B→ C?
- ZW-EQUIPOTENCE-009 The inclusion of ℕ in ℝ is an injective function. Why does it not prove that ℕsimℝ?