# What does the symbol $\lll$ mean?

$$A < B$$ 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?

• Can you provide an example of its use? – Andrew Uzzell Feb 11 '13 at 13:36
• If this symbol is actually used anywhere (I've never seen it), then certainly the author would have defined it previously. – David Mitra Feb 11 '13 at 13:48
• 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) – davidlowryduda Feb 11 '13 at 13:50
• I've found it in the LaTeX symbol list, and added a link in the question. – gerrit Feb 11 '13 at 13:52
• It means "very much less than"; what that means depends on the situation. – AakashM Feb 11 '13 at 15:07

## 2 Answers

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.

• Good answer, but why is it Community Wiki? – gerrit Feb 12 '13 at 8:34
• @gerrit Because the answerer felt he/she didn't deserve rep points – 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.

• 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?) – Darrel Hoffman Apr 3 '16 at 14:55