# Symbol for “if any”

I am looking for a symbol if any for the following equation in my algorithm

This is to find closed pattern where $p_i$ is longer than $p$ and $p$ is a sub-pattern of $p_i$ and $support(p) = support(p_i)$

so can I say

if $\forall \; p \subset p_i$ and $support(p) = support(p_i)$ or

if $\left | \{ p_i | p \subset p_i, support(p) = support(p_i) \} \right | > 0$

Or any other better way to represent?

-
Are you familliar with "If exists" ($\exists$) symbol? If I understood you correctly it might be what you need –  DanielY Oct 16 '13 at 5:48
That is a case of $\exists$, not of $\forall$. –  Marc van Leeuwen Oct 16 '13 at 5:50
if $∃pi : length(pi) = length(p) + 1 ∧ p ⊏ pi ∧ support(p) = support(pi)$ ? –  cherhan Oct 16 '13 at 5:53

The sentence

$\exists \pi\, P(\pi)$

translates to "there is a $\pi$ such that $\pi$ has property $P$." In your example we could take $P(\pi)$ to say $\text{length}(\pi) = \text{length}(p) + 1 \wedge \ldots.$

The sentence

If $\exists \pi\, P(\pi)$, then $Q$

translates to "if there is a $\pi$ such that $\pi$ has property $P$, then $Q$ is true." (You didn't say what the conclusion $Q$ would be in your case.) You could also write it more colloquially as "if some $\pi$ has property $P$, then $Q$ is true."

This sounds like what you want, unless to conclude $Q$ you need the stronger hypothesis that all $\pi$ have property $P$.

By the way, I would avoid using the word "any" in mathematical writing. It is usually clearer to use "some" or "all" depending on what you mean.

-
Thanks for your useful comment, it is more for an algorithm writing than mathematical writing. What I really want to mean is, if there exist $p_i$, where $length(p_i) = length(p) + 1$ and $p$ is a strict subset of $p_i$ –  cherhan Oct 16 '13 at 8:59