Base infinity

People of many disciplines look to mathematics for meaning and for truths about the physical world. I think people miss the obvious in this regard.

Would mathematics not become useless if you used a base infinity system as opposed to a base-finite system such as base ten? if so does it not seem like a message from the gods? only division creates meaning or something of the sort. im no mathematician but this seems obvious to me but im not sure. it seems like 2+2 would equal 4 if 1-4 was the first 4 characters but it feels like some of the more complex math would collapse. well just throwing this out there. ponder and let me know what you think. thanks