The meaning of $\rightsquigarrow$ in math? In order to write a scientific paper, I would like to use the symbol

\rightsquigarrow or \leadsto

which look as: $\rightsquigarrow$ or $\leadsto$
I'm wondering about the usual meaning and use of this symbol.
Thanks in advance.
 A: The semantic meaning of $\leadsto$ is literally "leads to". Some possible uses


*

*In solving a problem, it denotes "the next step is". For example, sometimes people write 
$$ (x - a)(x-c) = 0 \implies x-a = 0 $$
which is technically false. It makes a bit more sense to say that 
$$ (x-a)(x-c) = 0 \leadsto x-a = 0 $$
when elsewhere it has already been shown that $x-c \neq 0$. (Strictly speaking using \implies you need to write
$$ (x-c)\neq 0 \wedge (x-a)(x-c) = 0 \implies x-a = 0 $$
to be correct.)

*When describing an algorithm, the $\leadsto$ symbol is sometimes used to denote the next step, or the next transformation. For example, describing bubble sort I may write
$$ \underline{1,3},4,2 \leadsto 1,\underline{3,4},2 \leadsto 1,3,\underline{4,2} \leadsto \underline{1,3},2,\fbox{4} \leadsto 1,\underline{3,2},\fbox{4} \leadsto \underline{1,2},\fbox{3},\fbox{4} \leadsto \fbox{1},\fbox{2},\fbox{3},\fbox{4} $$

*Some logicians have very specific meanings attached to this symbol. Unfortunately my familiarity with respect to such is only "I've seen it in a book." 


But the symbol is often also co-opted for other meanings as well. As long as this symbol does not appear frequently in your field, you'll probably be okay if you just clearly define it to mean a certain thing in the beginning of your article and use it consistently. 
A: In topology, especially when used in algebraic geometry, $\leadsto$ means "to specialize to". We write $x_1\leadsto x_0$, where $x_0,x_1$ are two points of a topological space, if $x_0\in\overline{\{x_1\}}$, that is, every open neighbhourhood of $x_0$ contains $x_1$.
