Okay, I'm going to say this about infinity without dropping math equation bombs all over the place.

1. The basic premise of infinity is something that never ends. If there is a problem with this definition, webster it.
2. Infinity is NOT a specific number. It is an idea, and sometimes a state.
3. In order to achieve the ability to continue on for an infinite amount of time, there must be a 100% chance or greater to do so.
4. Infinity either IS or IS NOT. There is no middle ground. Either you have a 100% chance of being infinite, or you are finite.

Fancy math doesn't change this. The only way for this build to gain infinite attacks, is if it never suffers a miss on a natural 1. Even with luck rerolls, this is not possible. It doesn't matter how many attacks it generates, there is still a chance that you will roll 1 freakin godmillion 1's in a row and end your series. As long as that chance exists, you are not infinite.