# builder notation for set

• Sep 18th 2009, 06:31 PM
zpwnchen
builder notation for set
for this: {0,3,6,9,12}

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

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

Which one is correct and more valid?

and how to write for this one: {m,n,o,p} ?
• Sep 18th 2009, 10:23 PM
Set notation
Hello zpwnchen
Quote:

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

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

S={x|x is multiply of 3 and 0 $\leq$ x $\leq$ 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 $\mathbb{N}$, the natural numbers: it's either the positive integers, $\{1,2,3,...\}$ or the non-negative integers, $\{0,1,2,3,...\}$. So unless you state which of these two definitions is being used, then it's best to avoid using $\mathbb{N}$ here.

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

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