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I need a sign for an even number (not $a\cdot 2$) in my formula. I tried to google it, but I saw only $2a$. Please tell me if there is a special sign?

Zev Chonoles
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preslav
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    An integer $n$ is even iff $n=2k$ for some natural number $k$. That is, even numbers are characterized (or rather, defined) to be any number divisible by 2. That's all there is to it. No other signs, just divisibility by 2. – Paddling Ghost Jul 29 '15 at 16:23
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    You can write $n\in 2\mathbb Z$ for "$n$ is an even integer". – Hagen von Eitzen Jul 29 '15 at 16:24
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    how about $2 b$ ? seriously, I don't think there is one. You could however follow the strategy of the top answer here: http://math.stackexchange.com/questions/15556/is-zero-odd-or-even and make one up – Bort Jul 29 '15 at 16:24

2 Answers2

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We often like to say that an even number is any $2k$ for $k\in \mathbb Z$.

But another way is to use $\mathbb Z$ with scalar multiplication.

I.e. $\mathbb Z = \{..., -4, -3, -2, -1, 0, 1, 2, 3, 4, ...\}$. You know. The integers.

So $2\mathbb Z = \{..., -8, -6, -4, -2, 0, 2, 4, 6, 8, ...\}$ because every element in $\mathbb Z$ gets multiplied by $2$. This is now the set of all even numbers.

Now, you can refer to a number $n$ as even if $n \in 2\mathbb Z$.

Alec
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  • So would odd integers be (2ℤ + 1)? – Bob Marley Jun 14 '24 at 17:19
  • @BobMarley - No. Scalar multiplication with a set is defined by multiplying with all members of the set. But scalar addition is not defined, so we can't add a set and a number. For the odds, you could write it as ${ x \in \mathbb Z \ | \ x \text{ is odd } }$, or ${ 2k+1 \ | \ k \in \mathbb Z}$, for instance. – Alec Jun 15 '24 at 21:37
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As denoted in the answer to this question: Is zero odd or even?, $N_e$ is used to denote even numbers and $N_o$ for odd numbers. However, you could use any notation as long as it's clear to the reader what you are trying to symbolize with it.

Community
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SalmonKiller
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