Much less / much greater (≪ ≫) in LaTeX
\ll and \gg produce the double-chevron relations 'much less than' (≪) and 'much greater than' (≫), used when one quantity is an order of magnitude or more beyond another.
LaTeX command
\llNot the symbol you meant? Draw it to find the command →
These symbols are informal but standard: tells a reader to treat n as large enough that an approximation or expansion is valid, while \epsilon \ll 1 flags a small parameter being dropped from a series. There is no fixed numerical threshold; the meaning is set by the surrounding argument.
Don't confuse \ll and \gg with the plain strict inequalities < and >. They are separate relations with their own glyph and their own reading, reserved for scale comparisons rather than exact ordering, and they still need \ll / \gg as commands rather than two typed less-than signs.
In analytic number theory specifically, \ll is sometimes reused for Vinogradov notation, where means f(x) = O(g(x)) for large x. This is a different, more precise claim than the everyday 'much less than' reading, so state your convention if the audience might expect one or the other.
Other forms
\ggmuch greater (≫)Examples
$n \gg 1$n is much greater than 1, valid for a large-n approximation
$\epsilon \ll 1$epsilon is a small parameter, safe to expand around
$m \ll M$a small mass compared with a large mass
Tips and common mistakes
\lland\ggare built into LaTeX, no package needed.- Type the command, not two adjacent < or > characters; only
\ll/\gggive the correct double-chevron glyph and spacing. - In analytic number theory can mean Vinogradov's big-O notation rather than a literal scale comparison, make the convention explicit if it matters.
- For 'not much less than' there is no dedicated symbol;
\not\llproduces a slashed version if you need it.
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Convert your maths to LaTeX →FAQ
What does ≪ mean in maths?
'Much less than', an informal relation meaning one quantity is negligible compared with another, often used to justify dropping a term in an approximation.
What is the LaTeX code for ≫?
\gg. Its companion 'much less than' is \ll.
Is \ll the same as < in LaTeX?
No. < is the ordinary strict inequality; \ll is a separate double-chevron relation meaning much less than, used for scale rather than exact ordering.
How do I write 'not much less than'?
Use \not\ll, which draws a slash through the \ll symbol.