# Admissible absolute value on the integers #

This file defines an admissible absolute value absolute_value.abs_is_admissible which we use to show the class number of the ring of integers of a number field is finite.

## Main results #

• absolute_value.abs_is_admissible shows the "standard" absolute value on ℤ, mapping negative x to -x, is admissible.
theorem absolute_value.exists_partition_int (n : ) {ε : } (hε : 0 < ε) {b : } (hb : b 0) (A : fin n) :
∃ (t : fin nfin 1 / ε⌉₊), ∀ (i₀ i₁ : fin n), t i₀ = t i₁|A i₁ % b - A i₀ % b| < |b| ε

We can partition a finite family into partition_card ε sets, such that the remainders in each set are close together.

abs : ℤ → ℤ is an admissible absolute value

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@[instance]
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