1. ## Question

Hi everybody,

I have a question:

How can we write the set of real numbers odd and the set of real numbers

even?

And thank you anyway

2. Even numbers = $\displaystyle \{ 2n | n\in\mathbb{Z} \}$

Odd numbers = $\displaystyle \{ 2n+1 | n\in\mathbb{Z} \}$ where $\displaystyle \mathbb{Z}$ is the set of integers

3. Originally Posted by artvandalay11
Even numbers = $\displaystyle \{ 2n | n\in\mathbb{Z} \}$

Odd numbers = $\displaystyle \{ 2n+1 | n\in\mathbb{Z} \}$ where $\displaystyle \mathbb{Z}$ is the set of integers
That is certainly concise and precise. But could you not also just say
$\displaystyle \{ n| n \, even \in\mathbb{Z} \}$ or something similar? Wouldn't that actually be clearer?

4. Originally Posted by QM deFuturo
That is certainly concise and precise. But could you not also just say
$\displaystyle \{ n| n \, even \in\mathbb{Z} \}$ or something similar? Wouldn't that actually be clearer?

What I provided is the standard set notation for odds and evens as far as I know.

In terms of what you asked, why wouldnt you just write down $\displaystyle \in$Evens if you are going to use the word even,

The problem with that is you can define the odds and evens via set notation like I used, but you couldn't do that with what you said since you use the word even

but yes, I would have to say it would be correct to say n such that n is even, but it's redundant and doesn't tell you anything