# Plot a curve on a lattice

How do I plot a 2d curve and label lattice points to one side of it?

I want to plot the curve $f[x]=\frac{1}{x}$, and draw a solid red dot at every lattice point in the following set: $$\{(m,n)\in \mathbb N^2\colon mn\geq 1\}$$

• Make a lattice with Tuples, filter it with Select, plot with ListPlot, combine it with the curve using Show. Jul 23, 2015 at 6:37
• You can add something like Epilog -> {Red, Point[Flatten[Array[List, {5, 5}], 1]]} to your plot. Jul 23, 2015 at 6:41

In V10.1 or later, you can use CoordinateBoundingBoxArray to generate the lattice.
With[{m = 5},