[Round Two O.C.T.O.B.E.R. XVIII] Shorthand

Shorthand abounds everywhere.  On the Internet, many people communicate through “text speak.”  They use abbreviations, acronyms, and sometimes abbreviate phonetically.  This is not my modus operandi.  Rather, I tend to write how I speak, but that is another topic for another post.

When taking notes, I will often abbreviate certain words if I know that I will be able to decipher them later.  In my journal, abbreviations also occasionally appear when I write.  Of course, those abbreviations do not show up in my spoken language, as they are simply meant for writing more efficiently.

Shorthand, however, also appears in math to some sense.  Piecewise-defined functions, formally, are written with a “cases” bracket (I wish that WordPress supported LaTeX.  Instead, I had to create the equation through www.texify.com and then copy-and-paste the code there.)   For example, the seemingly-innocuous absolute value function is really a piecewise-defined function:

\left|x\right|=\begin{cases}x; & x \ge 0 \\-x; & x < 0\end{cases}

Sometimes, the shorthand will be dangerous if misused.  For example, suppose that you have a function defined as follows:

\varphi_{\pm}(z)=\begin{cases}\varphi_{1}; & \Im\left\lbrace z\right\rbrace > 0 \\\varphi_{2}; & \Im\left\lbrace z\right\rbrace < 0 \end{cases}

If a reflection is taken, you have to be careful as to the definition, since this is a different function in the upper half-plane versus the lower half-plane.  I was over-relying on this convenience notation, and overlooking a very important point with regards to it in my research.

So, although shorthand is convenient, you must be careful that it doesn’t hide an important property.  With writing in text, although most of the time you can understand the implied word, some abbreviations leave ambiguity without proper context.  The same thing goes for reading Hebrew without נקוד (vowels).

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Today is the eighteenth day of O.C.T.O.B.E.R.  That makes two weeks and four days.

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