Format mathematical definitions

Question

I want to define a list of definitions.

This is what I have:

\begin{align*}
Let & L_{1} = (Q_{1},\sum,\delta_{1},q_{1},F_{1}), and \\
& L_{2} = (Q_{2},\sum,\delta_{1},q_{2},F_{2}).
\end{align*}

I basically want it to say Let and then the two definitions to be lined up. But for some reason there is no space between Let on the first definition and also the sum symbol is huge.

Answer 1

I think you want to use the macro \Sigma instead of \sum. (The latter control word is an operator whose size increases in display-math environments such as align*; however, even if you typed {\textstyle\sum} you'd still get a symbol that's too large. Moreover, I think you're not trying to denote a summation operation anyway, right?) To align the two equations on the = sign, just prepend the & symbol to that sign:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
\text{Let } L_{1} &= (Q_{1},\Sigma,\delta_{1}, q_{1}, F_{1})\\
\text{and } L_{2} &= (Q_{2},\Sigma,\delta_{1}, q_{2}, F_{2})\,.
\end{align*}    
\end{document}

Addendum. Prompted by Andrew's comment about the symbol to use to denote definitional equality, I'll note that Scott Pakin observes on p. 23 of his Comprehensive LaTeX symbols list (paraphrasing slightly, to accommodate the present sentence structure) "that there are a variety of ways to indicate the mathematical notion of is defined as. Common candidates include \triangleq, \equiv, \coloneq (and several variants: in txfonts, pxfonts, and mathtools the symbol is called \coloneqq; in mathabx and MnSymbol it's called \coloneq; in colonequals it's called \colonequals) and \stackrel{\text{\tiny def}}{=}." In other words, there are at least four symbols to choose from when one wishes to denote definitional equality.

Answer 2

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
\makebox[2em][l]{Let} L_{1} &= (Q_{1},\Sigma,\delta_{1},q_{1}, F_{1})\\
\makebox[2em][l]{and} L_{2} &= (Q_{2},\Sigma,\delta_{1}, q_{2}, F_{2})\,.
\end{align*}    
\end{document}