Limit : The limit of a function $f$ for $x$ converging to $x_0$ or $\lim\limits_{x\to 0}f(x)$ is a number $y$ such that for every $\epsilon\gt 0$ there is a $\delta\gt 0$ with $|f(x)-y|\lt\epsilon$ for all $|x-x_0|\lt\delta.$ This means that if $x$ only gets close enough to $x_0$ it will get and stay arbitrarily close to $y.$

Norm : The norm $\lVert v\rVert$ of a vector $v=\begin{pmatrix}v_1\\v_2\\ \vdots \\v_n\\\end{pmatrix}$ is given by $\lVert v\rVert=\sqrt{v\cdot v}$ $=\sqrt{v_1^2+v_2^2+\ldots+v_n^2}.$ The norm of a vector intuitively describes the length of that vector.

Absolute value : The absolute value $|x|$ of a number $x$ is defined as the value of $x$ ignoring any potential minus sign. For example $|-2|=2$ and $|2|=2.$ In other words $|x|=x$ for $x\geq 0$ and $|x|=-x$ for $x\lt 0.$

Continuous : A function is continuous at a point $x_0$ if $\lim \limits_{x\to x_0} f(x)=f(x_0).$

Limit : The limit of a function $f$ for $x$ converging to $x_0$ or $\lim\limits_{x\to 0}f(x)$ is a number $y$ such that for every $\epsilon\gt 0$ there is a $\delta\gt 0$ with $|f(x)-y|\lt\epsilon$ for all $|x-x_0|\lt\delta.$ This means that if $x$ only gets close enough to $x_0$ it will get and stay arbitrarily close to $y.$

Limit : The limit of a function $f$ for $x$ converging to $x_0$ or $\lim\limits_{x\to 0}f(x)$ is a number $y$ such that for every $\epsilon\gt 0$ there is a $\delta\gt 0$ with $|f(x)-y|\lt\epsilon$ for all $|x-x_0|\lt\delta.$ This means that if $x$ only gets close enough to $x_0$ it will get and stay arbitrarily close to $y.$