Order of growth definition from Reynolds & Tymann
The paragraph is wrong. Unfortunately, it looks exactly like the kind of thing that a student who does not understand the material would write as an answer to an exercise. This sort of nonsense has no place in a textbook. Make no sudden movements. Put the book down. Step away from the book.


  We say that the "order of growth" of the sequential search algorithm is n. The notation for this is $T(n)$.


No. $T(n)$ is the notation for a function called $T$, which takes an argument called $n$. That function could be used to mean anything whatsoever. There is something of a tradition of writing recurrence relations for the running time of programs in the form, e.g.,
$$\begin{align*}
T(1)&amp;=k\\
T(n)&amp;=T(n-1)+\log n \quad\text{for }n&gt;1
\end{align*}$$
But $T$ is not an "order of growth", here: it is a specific function defined through a recurrence relation. And you cannot just write "$T(n)=\text{blah}$" and expect people to read your mind and know that the function&nbsp;$T$ denotes the running time of some algorithm.  $T$&nbsp;here stands for time.


  We also say that an algorithm whose order of growth is within some constant factor of $T(n)$ has a theta of NL say. "The sequential search has a theta of $n$."


This has obviously been mangled. I think the authors intended to write something like,


  We also say that an algorithm whose order of growth is within some constant factor of $T(n)$ has a theta of $\boldsymbol{n}$ and we say, "The sequential search has a theta of $n$."


But, please, we do not say "has a theta of $n$," just as, if $h$ is your notation for height, you wouldn't say "John has an $h$ of 180cm." It's just not a correct form of words. We actually say, "The running time of the algorithm is theta&nbsp;$n$ (or theta of&nbsp;$n$)." Note in particular, that $\Theta$ is a tool for talking about mathematical functions, not algorithms. Theta doesn't mean that the running time is something; rather, it's something you can use to talk about the running time.

"NL", by the way, denotes the complexity class nondeterministic logspace, which makes no sense at all in the position it appeared in the original quote.