I learned in high school from my favorite math teacher (who also has a PhD in mathematics) that the $\curvearrowright$ symbol means "implies that" (in German "daraus folgt"; "from that follows").
Now that I am learning higher math elsewhere I have not found this notation anywhere; it always seems to be the $\Rightarrow$ symbol.
The $\curvearrowright$ symbol has really grown on me, and it takes much less time to draw than the commonly used $\Rightarrow$ symbol.
I am just curious if $\curvearrowright$ is also a commonly accepted symbol? Maybe it's an old DDR (communist Germany) thing – as that's where my teacher received his PhD?
Best Answer
The commonly accepted symbols for implications are $\Rightarrow$ and its variation $\Longrightarrow$.
Objectively seen, it does not take much less time to draw $\curvearrowright$ than the commonly used $\Rightarrow$ symbol. The former one uses $15$ and the latter one $10$ letters in MathJax code. Also drawing it on paper does not make a real difference since a short line can be drawn in less than a second.
The only source I could find was in the German Wikipedia article, called "Folgepfeil" (implication arrow):
Then a long table of variations of the implication arrow follows, including $\curvearrowleft$ and $\curvearrowright$.
It is understandable that $\curvearrowright$ has a somewhat personal meaning to you, but I would refrain from using it. The curved arrow is not a commonly used symbol to denote an implication and therefore the usage of this symbol may lead to uncertainty of the reader.