Question:
What does the semicolon mean in "$(x(i), y(i)); i=1,\dots,m$"?
My Guess
"This is training example $(x_1, y_1)$ and it is in a set where $i$ is in the range $1$ to $m$".
Explanation:
I'm taking Andrew Ng's Machine Learning course on Coursera. He often uses math notation without explaining it.
This page has the paragraph ...
To establish notation for future use, we’ll use $x^{(i)}x (i)$ to denote the “input” variables (living area in this example), also called input features, and $y^{(i)}y (i)$ to denote the “output” or target variable that we are trying to predict (price). A pair $(x^{(i)}, y^{(i)})(x(i), y(i))$ is called a training example, and the dataset that we’ll be using to learn—a list of m training examples $(x(i),y(i));i=1,\dots,m$ — is called a training set. Note that the superscript “$(i)$” in the notation is simply an index into the training set, and has nothing to do with exponentiation. We will also use $X$ to denote the space of input values, and $Y$ to denote the space of output values. In this example, $X = Y = \mathbb{R}$.
This is a link to a screen shot of the above text. It's easier to read
