What is the Maths equation for positive integers? [closed]

$\begingroup$

I know there are equations for odd numbers . But is there an equation for positive integers.

$\endgroup$ 5

3 Answers

$\begingroup$

I'll answer based on my comment.

We can use the following notation to denote a positive odd integer:

• "$x$ is an odd positive integer $\iff x=2n−1\,$ for some $\,n\in \mathbb Z,n\geq 1$.

We can use the following notation to denote a positive even integer so,

• "$y$ is a positve even integer" $\iff y = 2n\,$ for some $\,n \in \mathbb Z,\,\,n\geq 1$

These notations reflect the definitions of odd positive integers, and even positive integers, respectively:

If we change the notation to exclude the qualifications $n\geq 1$ (so that $n$ is some integer), then we have defined odd and even integers, respectively, though when defining odd integers, in general, it is more common to define them as the set of all integers $x$ that can be expressed in the form $\;x = 2n +1$ for some $n \in \mathbb Z$.

Essentially, the notation reflects that an even integer, by definition, is an integer $x$ that is divisible by $2$, and odd integer is not.

$\endgroup$ $\begingroup$

An integer $m$ is odd $\iff$ there exists an integer $n$ such that $m=2n+1$. I don't think there is something similar to this for positive integers. Well, this is slightly more advanced, but an integer $n$ is nonnegative (positive or zero) $\iff$ there exist integers $a, b, c$, and $d$ so that $n=a^{2}+b^{2}+c^{2}+d^{2}$, and $n$ is positive $\iff$ not all four of them are zero. This result is Lagrange's four square theorem, but I imagine it wasn't what you're looking for.

$\endgroup$ 8 $\begingroup$

You can just say $x > 0$. As far as I know there isn't an algebraic statement that enforces positiveness throughout a calculation in quite the same manner that $2x$ enforces evenness.

Anyways, be careful not to confuse math notation for math.

$\endgroup$ 2