# Thread: builder notation for set

1. ## builder notation for set

for this: {0,3,6,9,12}

S={x|x $\displaystyle \in$ N , x is multiply of 3, x $\displaystyle \leq$ 12}

S={x|x is multiply of 3 and 0 $\displaystyle \leq$ x $\displaystyle \leq$ 12}

Which one is correct and more valid?

and how to write for this one: {m,n,o,p} ?

2. ## Set notation

Hello zpwnchen
Originally Posted by zpwnchen
for this: {0,3,6,9,12}

S={x|x $\displaystyle \in$ N , x is multiply of 3, x $\displaystyle \leq$ 12}

S={x|x is multiply of 3 and 0 $\displaystyle \leq$ x $\displaystyle \leq$ 12}

Which one is correct and more valid?

and how to write for this one: {m,n,o,p} ?
First, let's be clear that the word you want here is multiple, not multiply.

Secondly, there are two interpretations of $\displaystyle \mathbb{N}$, the natural numbers: it's either the positive integers, $\displaystyle \{1,2,3,...\}$ or the non-negative integers, $\displaystyle \{0,1,2,3,...\}$. So unless you state which of these two definitions is being used, then it's best to avoid using $\displaystyle \mathbb{N}$ here.

The clearest notation to use, then, is $\displaystyle S=\{x|x$ is a multiple of 3 and $\displaystyle 0\leq x \leq 12\}$.

You could define {m, n, o, p} in a variety of ways; for example, {$\displaystyle \lambda | \lambda$ is a lower-case letter and $\displaystyle \lambda$ follows l and precedes q in alphabetical order}