Cardinality Rule - Search Videos

What One-to-One Correspondence Shows ℤ⁺ and ℕ₀ Have the Same Cardinality? (7.4.9)

YouTubeMathematician

What One-to-One Correspondence Shows ℤ⁺ and ℕ₀ Have the Same Cardinality? (7.4.9)

I begin by observing that the only structural difference between the positive integers ℤ⁺ = {1, 2, 3, …} and the non-negative integers ℕ₀ = {0, 1, 2, …} is the presence of 0 in ℕ₀. Despite this, the sets have the same cardinality, so I construct an explicit bijection. I line up the elements of both sets and define a pairing: 1 ...

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