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20 lines
490 B
Agda
20 lines
490 B
Agda
{-# OPTIONS --safe --warning=error --without-K #-}
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open import Functions
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open import Numbers.Naturals.Semiring
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open import Sets.Cardinality.Finite.Definition
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module Sets.Cardinality.Countable.Definition where
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record CountablyInfiniteSet {a : _} (A : Set a) : Set a where
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field
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counting : A → ℕ
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countingIsBij : Bijection counting
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data Countable {a : _} (A : Set a) : Set a where
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finite : FiniteSet A → Countable A
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infinite : CountablyInfiniteSet A → Countable A
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