Okay, let's start with the Alignment
We're gonna use the following environment
\begin{array}
\end{array}
Here's an example
\begin{aligned}
a&=b\\
a^2&=ab\\
a^2-b^2&=ab-b^2\\
(a+b)(a-b)&=b(a-b)\\
a+b&=b\\
2b&=b\\
2&=1
\end{aligned}
As you can see, in each line, we put one "&" at the left side of the equal symbol.
At the end of each line, we put "\\" to start a new one.
Once done this, let's put the LaTeX's Tags and yields
Implies & Iff
We all know that we can type \Longrightarrow to generate& \Longleftrightarrow to generate
. We can short this, replacing that commands by \implies & \iff, which both of them generate the same.
\frac
Sometimes, we wanna write \frac{1}{2} to generate, we can also short this, writing the following: \frac12. Which generates the same. Be careful, for letters we must leave one space, so for example to write
, it writes \frac ab.
Another thing about fractions are examples like this
When we write another \frac, it should be \dfrac, otherwise, we're gonna get, which definitely is not nice.
--
To write limits, just put \lim_{x\to1}, or with letters \lim_{x\to a}.
Cases
To generate things like
was used the following environment
f(x)=|x|=\left\{\begin{array}{rr}x&\text{if }x\ge0\\
-x&\text{if }x<0\end{array}\right.
After the {array}, we have the {rr}, which means "right, right", this says how we want to align, we can also use {cr} which is "center, right", and many others.


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