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$A < B$ 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 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 $A \cdot B$ = $10^{10^{10}} \cdot 10^{10} \approx 10^{10^{10}+10} \approx 10^{10^{10}} \approx B$

...or does it mean something else?

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Can you provide an example of its use? –  Andrew Uzzell Feb 11 '13 at 13:36
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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) –  mixedmath 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
1  
It means "very much less than"; what that means depends on the situation. –  AakashM Feb 11 '13 at 15:07
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1 Answer

up vote 5 down vote accepted

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.

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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 at 20:49
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