| sequence |
\(x_1, \ldots,
x_n\) |
A sequence \(x_1\) to \(x_n\) |
| summation |
\(\sum_{i=1}^n
x_i\) or \(\displaystyle{\sum_{i=1}^n
x_i}\) |
The sum of the terms of the sequence \(x_1\) to \(x_n\) |
|
|
|
| all reals |
\(\mathbb{R}\) |
The (set of all) real numbers (numbers on
the number line) |
| all integers |
\(\mathbb{Z}\) |
The (set of all) integers (whole numbers
including negatives, zero, and positives) |
| all positive integers |
\(\mathbb{Z}^+\) |
The (set of all) strictly positive
integers |
| all natural numbers |
\(\mathbb{N}\) |
The (set of all) natural numbers.
Note: we use the convention that \(0\) is a natural number. |
|
|
|
| piecewise rule definition |
\(f(x) =
\begin{cases} x & \text{if~}x \geq 0 \\ -x &
\text{if~}x<0\end{cases}\) |
Define \(f\) of \(x\) to be \(x\) when \(x\) is nonnegative and to be \(-x\) when \(x\) is negative |
| function application |
\(f(7)\) |
\(f\) of
\(7\) or
\(f\) applied to \(7\) or the
image of \(7\) under \(f\) |
|
\(f(z)\) |
\(f\) of
\(z\) or
\(f\) applied to \(z\) or the
image of \(z\) under \(f\) |
|
\(f(g(z))\) |
\(f\) of
\(g\) of \(z\) or \(f\) applied to the result of \(g\) applied to \(z\) |
|
|
|
| absolute value |
\(\lvert -3
\rvert\) |
The absolute value of \(-3\) |
| square root |
\(\sqrt{9}\) |
The non-negative square root of \(9\) |
|
|
|