Exercise · ZW-EQUIPOTENCE-004 · ★★☆ Intermediate
Let \(\mathbb{N}=\{0,1,2,\dots\}\). Is \(\mathbb{N}\) equipotent to \(\{0,2,4,\dots\}\)?
Choose one option.
Show answer
- B. Yes, via \(n\mapsto 2n\)
Explanation
The function \(n\mapsto 2n\) is a bijection between \(\mathbb{N}\) and the evens. Being a proper part of an infinite set does not prevent equipotence.
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-003 Which of these properties does equipotence satisfy?
- 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?