# Notation: minimum for all (sub) elements

Have an element list \Delta, these Elements have sub values, \alpha, \beta, \gamma. I want to write: the minimum from the sub element \alpha, over all elements \Delta.

How can I write this mathematically correct (in latex)?

\min ...


thx

• Assuming $\Delta$ consists of triples $(\alpha,\beta,\gamma)$, you could do something like $\displaystyle\min_{(\alpha,\beta,\gamma)\in\Delta}\alpha$. May 19 at 19:02
• Thanks @Lorago Can I write it differently if there are too many variables in \Delta that don't all fit under min? The minimal element is only about the \alpha from \Delta.
– 2IRN
May 19 at 19:25
• How about $\displaystyle\min_{S\in\Delta}S_\alpha$, using subscript to denote the subvariables? May 19 at 21:59

The key part is to just be clear about what you mean. Since it's not clear what exactly $$\Delta$$ consists of, suppose $$\Delta$$ is some arbitrary collection of elements $$S$$, where we use $$S_\alpha$$ to denote the $$\alpha$$-component of $$S$$. Then we could write

$$\min_{S\in\Delta}S_\alpha$$

to denote the minimum of all $$\alpha$$'s. Another approach (which I do not like as much, but still works), would be to define a function

$$\phi:\Delta\to\mathbb{R},\quad S\mapsto S_\alpha,$$

i.e. $$\phi(S)$$ is the $$\alpha$$-value of $$S\in\Delta$$. We could then write

$$\min_{S\in\Delta}\phi(S).$$

Of course there are other ways to do it as well; the most important part is to be clear.