What does the symbol $\ll$ mean?

Question

I came across,

If $|y| \ll 1$, then $x/y$ may have large relative and absolute errors.

I'm not sure what the symbol $\ll$ means. I looked it up on Google and nothing came up.

$|y| << 1$ means "$y$ is a very small number". It's more or less the same as $y \to 0$. — Crostul, Aug 31 '16 at 22:31

score 2 · Answer 1 · answered Aug 31 '16 at 22:31

2

"... is very small compared to ..."

answered Aug 31 '16 at 22:31

Robert Israel

470,583

score 2 · Answer 2 · answered Aug 31 '16 at 22:47

In engineering and other not-so-strict applications of mathematics the symbol reads 'much less than'.

BTW, it does not consist of a two 'less-than' symbols (<< which renders as $<<$), it is a separate $\LaTeX$ symbol \ll rendering as $\ll$ (and its counterpart 'much greater than' is \gg $\gg$).

For more information and examples see e.g. Wikipedia:

R L W · Answer 3 · 2016-08-31T22:51:40.067

1

The symbol can be read as 'much less than'. Thus $|y| << 1$ means ' the absolute value of y is much less than 1'.

edited Aug 31 '16 at 22:51

answered Aug 31 '16 at 22:31

R L W

35

1

Not exactly. It means 'the absolute value of $y$ is much less than $1$'. – CiaPan Aug 31 '16 at 22:48
Oops! Thanks, edited now – R L W Aug 31 '16 at 22:51

What does the symbol $\ll$ mean?

3 Answers3