it just does ... it converges to a value.
such as if you were to summarize
1/2^n as n goes to infinity.
1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024+1/2048 ... yadda yadda yadda
Converges to 1, not infinity.
The joke about the mathematician never reaching the door is completely based on this. The mathmatician is too busy going half the distance to the door and adding it to what he has already done. However, the distance from him to the door is a constant and not infinite.
If that fucking blows your mind, look up
gabriel's horn. The formula for the surface area diverges to infinity, but the volume that the "horn" can hold is a constant value. However, the horn is also infinitely long.
So ... I can fill the "horn" to a point where it gets full. But I cannot paint the "horn" because it has infinite surface area.
If i were to use my theoretical quantum computer, I could calculate the exact volume
instantly, but get a buffer overflow for calculating surface area.
But this happens all the fucking time in computing. A problem is too complex or infinitely long even though it converges to a certain value when expressed discretely so an approximation is made.
Shit, forms of euler approximation appears all the time in video game code due to restrictions in computational power.
But a quantum computer ... wouldn't ever need to approximate.
We're talking game physics 10,000x more accurate with AI as smart as people and a quantum computer could run it as fast as your monitor could refresh. It would still puke if you divided by 0 though
(shit, actually im not so sure anymore if this is possible. simply because im not sure how you would code "loop infinity" ... ah. you could just make a case where the previous iteration matches the current one. Technically not "infinity" due to rounding error, but close enough. Actually, that wouldn't work because it could round off into a loop :/)