calculatorfunctionsnotation
In programming, often the value of True is also 1, and False is 0.
This means that:
(x>5)*4
will return 4 if x is greater than 5 (because (x>5)==1), else 0.
I need to accomplish a similar thing using mathematical operators (no piecewise functions, this has to be typed into Desmos calculator.)
Specifically, I need
$$
f(x)=\begin{cases} 1&&\text{if}~ x\leq n \\ 0&&\text{otherwise} \end{cases}
$$
without having to use piecewise notation. Here $n$ is a positive integer, as is $x$.
I think one reason is that often one does not want to remember what the variable names really represent.
As an example, when we choose to talk about the matrix $(a_{ij})$ instead of the matrix $(\mathrm{TransitionProbability}_{ij})$, this expresses the important fact that once we have formulated our problem in terms of matrices, it is perfectly safe to forget where the problem came from originally -- in fact, remembering what the matrix "really" describes might only be unnecessary psychological baggage that prevents us from applying all linear-algebraic tools at our disposal.
(As an aside, have you ever seen code written by a mathematician? It very often looks exactly like your first example.)
Updated, December 2018: I made the following website with the aim of producing a Desmos-like experience in 3D for my multivariable calculus students.
You can create and animate points, vectors, curves, surfaces (explicit & implicit), and vector fields. After creating a demonstration, you can save it and share.
Here are three scenes that I particularly like:
This project is on Github. If you find bugs or have ideas for improvements, please open an issue!
Best Answer
(Posted by Dave Radcliffe but then deleted):