$A < B$ means $A$ is smaller than $B$.
$A \ll B$ means $A$ is some orders of magnitude smaller than $B$ (see also this question for a more in-depth discussion). In modelling, it may mean that $A$ can be neglected ($A + B \approx B$).
In the $\mathrm\LaTeX$ amssymb symbol list, section Binary relations, I found the symbols $\lll$ and $\ggg$, spelt as \lll and \ggg, respectively. What does $A \lll B$ mean? An order of magnitude of order of magnitudes smaller? Does it mean $A \cdot B \approx B$ even if $A \gg 1$? Like in this example?
$B=10^{10^{10}}$ and $A=10^{10}$, then $A \cdot B$ = $10^{10^{10}} \cdot 10^{10} \approx 10^{10^{10}+10} \approx 10^{10^{10}} \approx B$.
$\ldots$or does it mean something else?
Best Answer
Quoting Mariano Suárez-Alvarez: