I think your use of infinity isn't particularly helpful here as it leads to the contradiction that knowing more doesn't lessen the knowledge gap, whereas it does appear to do so.
Maybe, a better interpretation would be that as we learn and understand more, we approach the limits of knowledge. Now it may take an infinite amount of knowledge to actually reach the limits of knowledge (c.f. an infinite series can approach a finite value, but takes forever to get there), but it can still be shown that we are getting nearer.
The other aspect is that as we understand more, we appreciate that there's even more to understand, but that can be thought of as our precision increasing and looking at the available knowledge in greater detail.
Maybe, a better interpretation would be that as we learn and understand more, we approach the limits of knowledge. Now it may take an infinite amount of knowledge to actually reach the limits of knowledge (c.f. an infinite series can approach a finite value, but takes forever to get there), but it can still be shown that we are getting nearer.
The other aspect is that as we understand more, we appreciate that there's even more to understand, but that can be thought of as our precision increasing and looking at the available knowledge in greater detail.