Definition:Odd Integer/Definition 1
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Definition
An integer $n \in \Z$ is odd if and only if it is not divisible by $2$.
That is, if and only if it is not even.
Euclid's Definition
In the words of Euclid:
- An odd number is that which is not divisible into two equal parts, or that which differs by an unit from an even number.
(The Elements: Book $\text{VII}$: Definition $7$)
Sequence of Odd Integers
The first few non-negative odd integers are:
- $1, 3, 5, 7, 9, 11, \ldots$
Also see
Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {IV}$: Rings and Fields: $24$. The Division Algorithm
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $2$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $2$
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): odd integer