First, consider how much any one person contributes to digital infinity. Digital implies discrete. We take all our art and knowledge, and turn it into ones and zeros. Each human's digital life is a mass of discrete bits of information. These discrete bits accumulate just as the discrete natural numbers \(\{0, 1, 2, 3, …\}\) accumulate.

Over time, as digitization technology develops, we gather finer and finer detail as well -- our files grow from megabytes, to gigabytes, to terabytes. We envision, generation after generation, an average person’s digital footprint growing, and, far enough into the future, accumulating beyond any finite discrete limit. In this sense, we imagine every individual contributing nothing more, and perhaps nothing less, than \(\mathbb{N}\) -- the discrete infinite -- to the larger set \(\mathscr{D}\).

And now we imagine an ever-growing population doing the same. The population grows and grows, surpassing every finite discrete number, up towards \(\mathbb{N}\). For our infinite set \(\mathscr{D}\), we imagine an infinite population; a population of \(\mathbb{N}\). And each individual, in this limit, may contribute as much as \(\mathbb{N}\) to \(\mathscr{D}\).

"We envision, generation after generation, an average person’s digital footprint growing, and, far enough into the future, accumulating beyond any finite discrete limit."