Update Sat Mar 2 04:21:56 UTC 2024

Math2001/Homework/hw5.lean

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+/- Copyright (c) Heather Macbeth, 2023.  All rights reserved. -/
+import Mathlib.Data.Real.Basic
+import Library.Basic
+import Library.Tactic.ModEq
+import AutograderLib
+
+-- BOTH:
+math2001_init
+
+/-! # Homework 5
+
+Don't forget to compare with the text version,
+https://github.com/hrmacbeth/math2001/wiki/Homework-5,
+for clearer statements and any special instructions. -/
+
+@[autograded 4]
+theorem problem1 : ∃ a : ℝ, ∀ b : ℝ, ∃ c : ℝ, a + c < b := by
+  sorry
+
+@[autograded 4]
+theorem problem2 : forall_sufficiently_large x : ℝ, x ^ 3 - 3 * x ≥ 12 * x ^ 2 := by
+  dsimp
+  sorry
+
+@[autograded 3]
+theorem problem3 (x : ℝ) : 3 * x + 1 = 10 ↔ x = 3 := by
+  sorry
+
+@[autograded 6]
+theorem problem4 (n : ℤ) : n ^ 2 + n + 3 ≡ 0 [ZMOD 5] ↔ n ≡ 1 [ZMOD 5] ∨ n ≡ 3 [ZMOD 5] := by
+  sorry
+
+@[autograded 4]
+theorem problem5 : ¬ (∃ t : ℝ, 2 * t ≤ 8 ∧ t ≥ 5) := by
+  sorry
+
+@[autograded 4]
+theorem problem6 : ¬ (∃ a : ℝ, ∀ b : ℝ, a ≤ b) := by
+  sorry