Infinity isn't something we can hope to understand yet. How can you add one to a number and it be the same? It follows none of the rules of normal numbers. If you add up all the integers and fractions before it you will get 0. (1-1) + (2-2) = 0.
We can't solve the problem of infinity because it CAN'T exist. There is ALWAYS a limiting factor to everything. Amount of space, amount of paper, amount of particles in the universe! If there is always a limiting factor, then nothing can be endless. So infinity is a game, not a possibility.