I ran over a problem with desmos after playing around with floor functions and want to know what is my thinking error or if the problem lies with Desmos.
In the Screenshot you can see the function floor(x)-floor(y)=0. I tested the function at the point (1.2,1.4) manually and it was true, but the point is not part of the graph.
What are your thoughts on this?
On
It is not difficult to show that $\lfloor x\rfloor=\lfloor y\rfloor$ if and only if $(x-\lfloor y\rfloor)(y-\lfloor x\rfloor)\ge0$.
Try graphing in Desmos
$$ (x-\lfloor y\rfloor)(y- \lfloor x\rfloor)\ge0$$
Desmos does not show it accurately on the boundaries, however.
It is also the case that $\lfloor y\rfloor=\lfloor x\rfloor$ if and only if $\vert \lfloor y\rfloor-\lfloor x\rfloor \vert <1$, but Desmos errs once again on the boundary.
It is an error (see my comment). You can graph
$$\lfloor x\rfloor=\lfloor y\rfloor$$
on Desmos.com by looking at the complement of
$$\{ (x,y) | \lfloor x\rfloor<\lfloor y\rfloor \} \cup \{ (x,y) | \lfloor x\rfloor>\lfloor y\rfloor \}$$
The Unshaded region below is the graph of your equation.
Alternatively, taking the complement of
$$\left|\lfloor x\rfloor-\lfloor y\rfloor\right|>0$$