Have you heard about Zeno’s paradoxes (Achilles and the Tortoise and The Arrow Paradox). Check them out. Well I have thought of one now. It is “You have half a circle then you add half of that and then half of that and keep on going.” Here is a demonstration.
No matter how many times you add another half it will still never reach one. When you think of it being fractions the pattern is 1/2, 3/4, 7/8, 15/16, 31/32, 63/64 and so on. The denominator is two to the power of whatever stage and the numerator is the denominator minus one. To show it in algebra, Number of Stage=S, Numerator=N and Denominator=D. The equations are D=2^S and N=D-1. ^ means to the power of. In decimals it is 0.5, 0.75, 0.875, 0.9375, 0.96875, 0.984375. You would think Infinity times a number equals Infinity but in this case it equals one.