Lecture 5 Number Theory & Proof Methods

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Presentation transcript:

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

Odd and Even Numbers

Prime and Composite numbers

Example

How to (dis)approve

Disproof by Counterexample

Proving Universal Statements

Direct Proofs

Example

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

Rational & Irrational numbers

Integers are rational numbers

Proving properties of rational numbers

What is divisibility

Divisibility of Algebraic expressions

Transitivity of Divisibility

Exercises

Counterexamples & Divisibility

Quotient-Remainder Theorem

Div and Mod

Div & Mod

Floor & Ceiling

Floor & Ceiling

Floor & Ceiling

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