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

Continuous function : A function is continuous if it is continuous at every point $x.$ The graph of a continuous function does not have any jumps.

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 $y.$

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

Continuous function : A function is continuous if it is continuous at every point $x.$ The graph of a continuous function does not have any jumps.

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 $y.$

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

Function : A function is a mapping in which every element in one set is mapped to exactly one element of a second set. Most often the mapping is described using a rule. For example the function $f(x)=x+1$ maps 2 to 3 and -1 to 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 $y.$

Point : A point is an element in a space. Shapes are made of sets of points.