I am reading


* imenez, J., Echevarria, J.I., Sousa, T. and Gutierrez, D. (2012), *SMAA: Enhanced Subpixel Morphological Antialiasing* Computer Graphics Forum, 31: 355-364. <https://doi.org/10.1111/j.1467-8659.2012.03014.x>


where I have encountered these three equations


\begin{gather\*}
e\_l=\lvert L-L\_l\rvert>T \\
c\_\text{max} = \max(c\_t, c\_r,c\_l,c\_r,c\_{2l}) \\
e\_{l'}=e\_l \land c\_l > 0.5 c\_\text{max}.
\end{gather\*}


Because $e\_l$ is a number being either 0 or 1, and $c\_l$ is always going to be a fraction number, I am wondering what is the AND result of these two? Would it be either 1 or 0 or it is going to be the value of $c\_l$ when $e\_l$ is 1?



Can you do boolean and of 1 and a number less than 1?
The paragraph before says



> 
> We calculate the maximum contrast $c\_{max}$ for all these edges and compare it with the contrast for the left edge [this is $c\_l$]. If the latter is above a threshold of $0.5\cdot c\_{max}$ the edge is preserved; otherwise, it is ignored.
> 
> 
> 


So this reads to me like a condition $c\_l \gt 0.5\cdot c\_{max}$.


We also have the definition of $e\_l$:



> 
> a straightforward algorithm would calculate $e\_l=|L−L\_l|\gt T$, where $e\_l$ is the **boolean value** that codes whether the edge is active, [emphasis added]
> 
> 
> 


so we should think of $e\_l$ not as $0$ or $1$, but a *boolean*, $T$ or $F$, giving the truth value of the condition "$|L−L\_l|\gt T$", which may or may not be true.


Moreover, after he displayed formulas, we have



> 
> where $c\_t$, $c\_r$, $c\_b$, $c\_l$, $c\_{2l}$ are the contrast deltas for the edges shown in Figure 5, and $e'\_l$ represents the final boolean value (active or not) for the left edge boundary.
> 
> 
> 


so again, we have that $e'\_l$ is a boolean, and so the condition $e\_l = e'\_l$ is checking if two booleans are equal (i.e. both true or both false).


The paper is using a symbol, $\wedge$, where a word would do, in a false economy, or else insisting on avoiding a word in an equation environment.


