# What does the symbol <<< mean? [duplicate]

Can anyone give the LaTeX code for the unusual symbol <<<, and perhaps provide some good examples of its use?

Does it mean "much much less than"?

• Try \lll which gives $\lll$. Aug 3, 2015 at 16:19
• I'm not sure what the common uses of that symbol are, because $\ll$ already means "very much less than" in a way that is hopefully clear from the context, e.g. saying that the ratio of the left-side to the right-side goes to $0$ in some limit, for example. Or, that given the right-side, the left-side is less than some very small function of the right-side. So if we already use $\ll$, I don't know what "extra meaning" that $\lll$ could have. Note the use of $\ll$ is already somewhat ambiguous enough to discourage its use in rigorous math proofs. But I see it in physics and stats arguments. Aug 3, 2015 at 16:22
• Isn't $\ll$ used for "Big-O" notation sometimes ... I seem to remember this from somewhere... Aug 3, 2015 at 16:40

From a cursory search, it appears that the triple less-than sign $\lll$ is not often used in a mathematical context but in a programming one (maybe an experienced programmer or two can weigh in). From the wiki page:
• In PHP, operator <<<OUTPUT is used to denote the beginning of a heredoc statement (where OUTPUT is an arbitrary named variable).
• In Bash, <<<word is used as a "here string," where word is expanded and supplied to the command on its standard input, similar to a heredoc.
At least in mathematics, it is clear that something like $a\ll b$ means "$a$ is much less than $b$." Other than that, however, it does not appear that the symbol $\lll$ is used in mathematical contexts (none that I have seen anyway). A look at the wiki page on inequalities yields similarly fruitless results for trying to find that symbol/notation in math.