Equations in LaTeX, Part 6

LaTeX experts will probably consider all the examples you'll find on
this page to be little more than hacks, but that's okay, because I
agree. But, at least, they are hacks that worked for me. By the way,
when you see the macro '\no' it stands for '\noindent'. When you
see the macro '\dis' it stands for '\displaystyle'. If you want to use
those shorter macros, you'll have to define them yourself (it's easy).

I often use the displaystyle, where others might not, because in some modes,
the math lookes too vertically compressed. This can happen when you do inline
math, especially for fractions and squareroot signs. But it can also happen in
displayed equation, when you nest fgractions in fractions, of squaretroots
in numerators or denominators.

---

For the first illustration, we have a 'roman numeral X', which I
cobbled together to get

The code for this is:

\begin{equation}
     \romanX^2 - 2xu \romanX -1 = 0 \,.
\end{equation}

(Clearly, I'm not using this symbol for the roman numeral for 10, but as a variable.)

But this code uses the definitions below (which can be placed in the preamble
of the LaTeX page):

    \def\topline{\raisebox{6.5pt}{\rule{2.8mm}{.6pt}}}
    \def\bottomline{\raisebox{0pt}{\rule{2.8mm}{.6pt}}}
    \def\romanX{\mbox{X}\kern-8pt\topline\kern-8pt\bottomline}

Or, you can write these using the \newcommand command.

Anyway, as you can see, you have to go by trial and error to get the top and
bottom lines the thickness and exact placement that looks good to your eye.

There are packages to do roman numerals, but 1) I could not get the one I
tried to work right, and 2) the X numeral was not what I had expected. So I
constructed my own version of it.

---

Next, I wanted to rescale a mathematical symbol arbitrarily large, but it turned out
that it only needed to be enlarged 1.2 times. The ability to do this resides in the
\scalebox command. The syntax is as this:

\scalebox{scaling factor}{thing to be rescaled}

So, when I went to rescale the symbol for the 'unity' symbol, I used

\def\unity{\scalebox{1.2}{$\mathbb{1}$}}

and then typed in '\unity'. The result is this:
By the way, \mathbb stands for "math blackboard bold".

---

I wanted to make my own symbol to represent an ideal of a ring. I chose
to the hollow-tipped left-pointing arrow. So, I had to construct it, and
it wasn't hard. I used this

$\triangleleft\hskip-5pt-$

which looks like this: .
The command '\hskip-5pt' means to move the printhead (sotospeak) 5 points to the left.

---

There is always something new to learn when typesetting mathematics in LaTeX.
How should we typeset the following: ? I used this:

\lim_{\overset{\scalebox{0.75}{$t\to +\infty$}}{t'\to-\infty}}

To use the \overset command, one thing is placed over another thing, but in this case
in a different size. So I used the \scalebox command to adjust them to be the same size.
The adjustment is trial and error. As usual, there's probably a better way to do this.