## Digital Sketch: Number of Subsets

I remember a particular book that I used to flip through often when I was a kid. It was called *Proof by Pictures*, or something to that effect. I was *fascinated* that someone could prove something without saying a word. The “proof” may not always be clear --- when it is, it is quite charming, and when it isn't, it can usually be treated as a worthy puzzle on its own right.

As a tribute to this bit of nostalgia, here's a wallpaper explaining one of the earliest facts one encounters in discrete mathematics, namely that the total number of subsets of an $n$-element set is $2^n$. There are any number of ways of proving this, and I have attempted to capture the one by induction --- in particular, the one where we observe that the new element either belongs, or does not belong, to one of the old subsets (that are made available inductively).

I am very much the vector graphics noob, so I stuck to the basics mostly out of lack of choice :) There is nothing fancy going on here --- the only thing that may not be immediate is the half-colored star, which was obtained by overlaying a suitably shaped object and using Object → Clip → Set (this pretty much amounts to cropping your original object).