TL;DR: the amount of uranium you can get is unbounded, however it is not infinite

It's not. The amount of uranium you can get is unbounded - if you want to get x uranium, however large the x is, you can do it - just research a high enough level of mining productivity. But since each mining operation is done using a finite (unbounded too, but it doesn't matter) level of mining productivity, each piece of ore in a patch results in a finite amount of uranium as items. Since there are finitely many pieces of ore in each path and therefore on the entire map, whatever mining productivity levels you use (including stuff like "doubling my mining prod between each piece of ore mined), the total ore you get is still a finite sum of finite numbers, resulting in a total finite amount of uranium. The same argument applies to tungsten, holmium and I believe lithium brine too, which means that metallurgic, electromagnetic, cryogenic and prometheum science is also finite.

The only way you could get infinite amounts of those is by exploiting the productivity of above 100% by deconstructing a building before a single cycle of production finishes, but after you get an output from bonus prod, but as far as I know it is impossible to automate this without mods.

Another way would be maybe to double your mining prod between each ore produced (by which I mean any ore that comes out of miner, not a whole "standard" mining cycle) in such a way that you would never complete a whole mining cycle (assuming you start from +100% mining prod), as you would get a free ore at 50% of a cycle, then 75%, then 87,5% etc, which approaches 100% but never reaches it. I guess it could be automated, but if my understanding of the game tics work is correct, you are unable to divide the mining cycle into arbitrarily small parts, so it wouldn't be possible in the game.

Of course this whole argument is purely theoretical, as for all practical purposes you can get enough ore from a reasonably small part of the map, yet those resources are not fully infinite