$A < B$ 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?

  • $\begingroup$ Can you provide an example of its use? $\endgroup$ – Andrew Uzzell Feb 11 '13 at 13:36
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    $\begingroup$ If this symbol is actually used anywhere (I've never seen it), then certainly the author would have defined it previously. $\endgroup$ – David Mitra Feb 11 '13 at 13:48
  • $\begingroup$ I've never seen the symbol either (and I use the second symbol differently than you do). I suspect it was defined in whatever text you are reading. (edit: In other words, I agree with David Mitra) $\endgroup$ – davidlowryduda Feb 11 '13 at 13:50
  • $\begingroup$ I've found it in the LaTeX symbol list, and added a link in the question. $\endgroup$ – gerrit Feb 11 '13 at 13:52
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    $\begingroup$ It means "very much less than"; what that means depends on the situation. $\endgroup$ – AakashM Feb 11 '13 at 15:07

Quoting Mariano Suárez-Alvarez:

The symbol denotes whatever the author tells you it will denote in his comments about notation, and there is a special place in hell for users of unexplained notation.

  • $\begingroup$ Good answer, but why is it Community Wiki? $\endgroup$ – gerrit Feb 12 '13 at 8:34
  • $\begingroup$ @gerrit Because the answerer felt he/she didn't deserve rep points $\endgroup$ – Rustyn Mar 26 '14 at 20:49

Mariano Suárez-Alvarez's comment gives the correct answer that the usage of $\lll$ or $\ggg$ is nonstandard and will have to be defined in-context, but it might be of interest that several sources use these symbols to denote bitwise shifts. See examples here, here, and here.

  • $\begingroup$ Java has a >>> operator, but does not have <<<. In any case, I doubt that's the intended use in the OP's case, as >>> is not the same as . (Also, your links are behind a pay-wall - can you find any examples that are free to view?) $\endgroup$ – Darrel Hoffman Apr 3 '16 at 14:55

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