Add sorry's to Apostol exercise set.

finite-set-exercises
Joshua Potter 2023-04-23 08:52:37 -06:00
parent fdc5936766
commit 677420afe0
2 changed files with 21 additions and 2 deletions

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@ -1 +1,2 @@
import OneVariableCalculus.Exercises.Exercises_I_3_12 import OneVariableCalculus.Exercises.Exercises_I_3_12
import OneVariableCalculus.Exercises.Exercises_1_7

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@ -1,6 +1,11 @@
/- /-
Exercises 1.7 Exercises 1.7
-/ -/
import OneVariableCalculus.Real.Geometry.Area
import OneVariableCalculus.Real.Geometry.Rectangle
open Real
open Real.Geometry.Area
-- ======================================== -- ========================================
-- The properties of area in this set of exercises are to be deduced from the -- The properties of area in this set of exercises are to be deduced from the
@ -16,7 +21,20 @@ Exercises 1.7
-- (c) The union of a finite collection of line segments in a plane. -- (c) The union of a finite collection of line segments in a plane.
-- ---------------------------------------- -- ----------------------------------------
-- # TODO example (p : Point)
: p.set_def ∈ 𝓜
∧ ((h : p.set_def ∈ 𝓜) → area h = 0) :=
sorry
example (S : Set Point) (hf : Set.Finite S)
: ( p ∈ S, p.set_def) ∈ 𝓜
∧ ((h : ( p ∈ S, p.set_def) ∈ 𝓜) → area h = 0) :=
sorry
example (S : Set LineSegment) (hf : Set.Finite S)
: ( s ∈ S, s.set_def) ∈ 𝓜
∧ ((h : ( s ∈ S, s.set_def) ∈ 𝓜) → area h = 0) :=
sorry
-- ---------------------------------------- -- ----------------------------------------
-- Exercise 2 -- Exercise 2