What do $\gg$ and $\ll$ mean? 
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What does $\ll$ mean? 


What do $\gg$ and $\ll$ mean?

I don't know how to search them for the net. Thank you.
 A: In C++ they are used to denote right and left shift as a bitwise operation.
EDIT: This answer was posted as answer to the original question, which contained $<<$ and $>>$. This notation (at least to me) is more naturally linked to the bitwise operations. Since then the post was edited and these symbols were changed to $\ll$ and $\gg$. (Which is the form of the question at this moment.) But this edit was not made by the OP and the OP neither mentioned in comments whether this is what he wanted to write nor edited his post. So we cannot be sure that this was really the way the question was intended.
A: E.g. Claim A holds for $n>>0$ means that $\exists n_0$: Claim A holds for all $n\geq n_0$.  
A: In programming in C-like languages they denote bitwise right shift/left shift. The binary number 00010111 left shifted two steps is 01011100, written 23<<2 (which is 92). Similarly, 23>>2 is 00000101 which is 5.
A: This is Vinogradov notation. $f(n)\ll g(n)$ means that there is some $k>0$ such that for all large $n$, $f(n)<k\cdot g(n).$ This is the same as writing $f(n)=O(g(n)).$
Of course this is entirely different from C's << bit shift operator which multiplies by the indicated power of two.
A: If it is used in comparing two positive values $x$ and $y$, $x \ll y$  implies that $x$ is much less than $y$ and $y \gg x$ implies that $y$ is much greater than $x$.
Note that $x \ll y \iff y \gg x$ so these properties may be applied $x\ll y$


*

*$\cfrac xy \simeq 0$

*$x +y \simeq y$

