4.2 Definitions

Class: CSE 16 Subject: computer-science discrete-math Date: 2024-11-02 Teacher: Prof. Musacchio

Direct Proof

Def 1: Even

• An integer $n$ is even if $n=2a$ for some integer $a\in \mathbb{Z}$

Def 2: Odd

• An integer $n$ is odd if $n=2a$ + 1 for some integer $a\in \mathbb{Z}$

Def 3: Parity

• Two integers have the same parity if they are both even or they are both odd. Otherwise they have opposite parity.

Def 4

• Suppose $a$ and b are integers. We say that $a$ divides $b$, written $a|b$, if $b=ac$ for some $c\in \mathbb{Z}$. In this case we also say that $a$ is a divisor of $b$, and that $b$ is a multiple of $a$.