You are right: computational errors due to the finite precision of binary computers, when representing irrational numbers like pi, serve as an counterargument for the hypothesis that our world is a simulated mathematical universe.
See one of the last chapters from Greene, Brian: The Hidden reality.
What do you mean by "virtual infinity"?
Assume a certain law of nature is the solution of a differential equation. The digital computer can alculate the solution as an extrapolation into the future only with finite precision, Hence in the course of time the simulated solution necessarily will deviate from the observed law of nature by an increasing amount. The error may become arbitrary big. Such that we observe anomalies even in the mesocosmic domain.
In the long run the simulated results do not follow the laws, which we consider laws of nature. And due to the finite precision we get a random distribution of rounding errors. Hence the anomalies do not follow a common scheme as were to be expected, when the only reason were a slightly different law of nature.
These are the arguments, why we do not live in a virtual wold simulated by a digital computer, see Greene, Brian: The Hidden Reality. 2014