> There is no contradiction because there is no limit of knowledge.
I don't think we know enough to be able to state that definitively. It's feasible that the universe behaves mathematically (it seems to so far) and thus possible to gain a thorough understanding of the underlying principles, if not the specific facts (c.f. with understanding how to produce integers yet not "knowing" all the integers).
Even if the universe doesn't have underlying rules to be discovered, there's still a limit to number of configurations available to particles etc. within our visible universe. Although that number might appear to be infinite to us, it's actually drastically closer to zero than to infinity.
So, if there is indeed some finite limit, then using y = e^x would be the wrong function as that doesn't approach a finite value.
I don't think we know enough to be able to state that definitively. It's feasible that the universe behaves mathematically (it seems to so far) and thus possible to gain a thorough understanding of the underlying principles, if not the specific facts (c.f. with understanding how to produce integers yet not "knowing" all the integers).
Even if the universe doesn't have underlying rules to be discovered, there's still a limit to number of configurations available to particles etc. within our visible universe. Although that number might appear to be infinite to us, it's actually drastically closer to zero than to infinity.
So, if there is indeed some finite limit, then using y = e^x would be the wrong function as that doesn't approach a finite value.