Mathematical notation $\max$ with simple example for non-mathematician First, let me start off by saying I'm not a mathematician so I'm going to need this explained to me at a pretty basic, almost intuitive level.  I've taken Calculus but it's been some time so I do have some math background.
I was reading a book tonight and there was a section on the minimax principle in game theory.  There was some notation in the book that I don't know what it mean.  Can someone explain, in words, what something like the following would mean?
$\underset{\theta\in\Theta}{\max}R_{T}(\theta)$
Does this mean the value of theta in the parameter space that maximizes the function $R_T(\theta)?$  Could you provide a simple example?
Then, in the full context, the book reads that T is the minimax if:
$\underset{T_{1}}{\min}\,\underset{\theta\in\Theta}{\max}R_{T_{1}}(\theta)$
Thanks.

$$\max_{\theta\in\Theta}R_T(\theta)$$means the maximum value that $R_T(\theta)$ can take as $\theta$ varies over all possible values in $\Theta$. This quantity is still dependent on $T$, and its least value for all possible values of $T$ is $$\min_{T}\max_{\theta\in\Theta}R_T(\theta).$$ Here the possible values for $T$ are assumed to be understood, and not made explicit. Also, the meaning is the same if the letter $T$ is replaced  by $T_1$ or some other appropriate symbol.
