How to typeset piecewise functions [duplicate]

Question

I don't know what the big { thing is called so can't search and when tried and write in LaTeX and didn't find this expression or structure in word either.

Answer 1

\documentclass{article}
\usepackage{mathtools}          %loads amsmath as well
\DeclarePairedDelimiter\Floor\lfloor\rfloor
\DeclarePairedDelimiter\Ceil\lceil\rceil

\begin{document}
\[
  T(n) =
  \begin{cases}
                                   0 & \text{if $n=1$} \\
                                   1 & \text{if $n=2$} \\
  T(\Floor{n/2}) + T(\Ceil{n/2}) + 2 & \text{if $n>2$}
  \end{cases}
\]
\end{document}

Answer 2

With only a partial alignment, due to the long last line:

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{fourier}
\usepackage{mathtools} %loads amsmath as well
\DeclarePairedDelimiter\Floor⎣⎦
\DeclarePairedDelimiter\Ceil⎣⎦

\begin{document}

\[ T(n) =
  \begin{cases*}
    0 \quad& if $ n = 1 $ \\
    1 & if $ n = 2 $ \\
    \mathrlap{T(\Floor{n/2}) + T(\Ceil{n/2}) + 2 \quad \text{if } n > 2}
  \end{cases*}\]

\end{document} 

Answer 3

This is one way to obtain the desired result in LaTeX

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{align}
T(n) = \left\{ \begin{array}{cc} 
                0 & \hspace{5mm} n=1 \\
                1 & \hspace{5mm} n=2 \\
                T( \lfloor \frac{n}{2} \rfloor) + T(\lceil \frac{n}{2} \rceil
                      )+ 2 & \hspace{5mm} n > 2 \\
                \end{array} \right.
\end{align}

\end{document}