1. Lecture 5 Number Theory & Proof Methods
Discrete Structures
Lecture 5
Number Theory & Proof Methods

2. Odd and Even Numbers

3. Prime and Composite numbers

4. Example

5. How to (dis)approve

6. Disproof by Counterexample

7. Proving Universal Statements

8. Direct Proofs

9. Example

10. Example
If a is any even integer and b is any odd integer, then is an integer.

11. Rational & Irrational numbers

12. Integers are rational numbers

13. Proving properties of rational numbers

14. What is divisibility

15. Divisibility of Algebraic expressions

16. Transitivity of Divisibility

17. Exercises

18. Counterexamples & Divisibility

19. Quotient-Remainder Theorem

20. Div and Mod

21. Div & Mod

24. Floor & Ceiling

25. Floor & Ceiling

26. Floor & Ceiling