[estsauver]

The way many things relating to infinity in math are described is something like this:

You get to pick a size of tile. You can pick whatever you want, totally independently. 700x700, 1000000x1000000, whatever, it's fine.

If I can describe a mapping for that arbitrary size tile, then I'm able to map an "infinitely" large plane. That even as we approach infinity, no matter the size of the finite plane, I can make an arrangement of tiles that fully covers the plane, means I've "infinitely" mapped the plane. (In some cases where there's uncertainty you might say something more like we've shown that the limit as plane size approaches infinity is mappable.)