Does halving ever end?
It will, one day, reach 0, which mean mining wont be possible anymore (or it wont just be worth it). and by 0, I mean it could be 0.000001.

But if you look at it in a mathematical way, it should never end. Try that with a calculator, the number becomes really small.

The Bitcoin network is made so there will be a limited number of coins available and they have to be generated at a predictable rate, thats also why there is a difficulty on the mining