TITLE: Much less than, what does that mean?
QUESTION [101 upvotes]: What exactly does $\ll$ mean?
I am familiar that this symbol means much less than. 
...but what exactly does "much less than" mean? (Or the corollary, $\gg$)
On Wikipedia, the example they use is that $1\ll 9999999999$
But my thought on that is that $10^{10^{10^{11}}}\ll 10^{10^{10^{11}}}+9999999999$, based on the same logic. But I am confused because the numbers are comparitively. 
Logically, I am really kinda spent dealing with this issue of mine. Thanks for any input.

REPLY [4 votes]: A (too) simple definition would be
$$
a \ll b ~ \Leftrightarrow ~ \frac{a}{b} \approx 0
$$
There may be some context implied: a variable tending toward $0$ or $\infty$, or a certain imprecision level that the user is willing to accept.