Exercise · ZW-EQUIPOTENCE-006 · ★☆☆ Basic
How is it written that the sets \(A\) and \(B\) are equipotent?
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Explanation
The symbol \(\sim\) denotes equipotence. The other three express proper inclusion, membership and disjointness.
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-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-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?