Handouts on Basic Proofs for M 325K, Spring 2024

---

---

Click on the desired handout name.

---

---

• Theorems (NIB) 1, 2, & 3

• Handouts attached to this one:

  • The Unique Prime Factorization Theorem
  • Applying Theorem (NIB) 2 in a Proof

• The Quotient-Remainder Theorem and the Definitions of (n mod d) and (n div d)

• Handout attached to this one:

  • Example Proofs Involving the (n mod d)-Function
• Example Proofs Involving Divisibility
• Proof of Theorem 4.3.1
• Proof that the Sum of Two Rational Numbers is a Rational Number
• The Ground Rules (and Other Rules) of Proof Writing
• The Method of Direct Proof (Used Only for Proving Universal Statements)
• Common Mistakes (with Commentary), as presented in class
• Basic Assumptions for Proof-Writing in this Course
• In-the-Book Definitions (I)

---

---