Integers and addition

ImportantTo do

• Read §1 The integers, §2 Rules for addition
• Before each proof of N3, N4, N5: cover it, try it yourself
• §2 exercises: 1, 3, 5, 7, 9, 11, 12, 13, 14, 16, 18, 20, ★22, ★23
• Paper: all listed exercises. Mark ✓ / ✗ / S. Answers: back of the book.
• Notebook: write each div below in your own words. Copy the ★ exercises in clean.

Definition 1 (Integer (celé číslo)) Your words.

Definition 2 (Additive inverse (opačné číslo)) Your words.

Definition 3 (Commutativity (komutativita) and associativity (asociativita) of addition) Your words.

Theorem 1 (N3: uniqueness of the additive inverse) Your words.

Proof. Cover the book’s proof. Try 10–15 min first.

Theorem 2 (N4: minus minus a) Your words.

Proof. Cover the book’s proof. Try 10–15 min first.

Theorem 3 (N5: minus of a sum) Your words.

Proof. Cover the book’s proof. Try 10–15 min first.

TipIntuition

Your words.

Exercises

★ 22. Prove the cancellation law (zákon o krácení) for addition: if a + b = a + c, then b = c.

NoteSolution

Your words.

★ 23. Prove: if a + b = a, then b = 0.

NoteSolution

Your words.