Puzzling

One of the prevalent paradoxes in the world of Physics/Philosophy/Mathematics is the following idea:

Suppose that you want to cross the room and touch the wall on the other side of the room. Ok, now imagine that you want to find the mid point between you and the wall. Next, you want to find the mid point of the two halves of the distance (now you have fourths of your path). Mathematically, this can be done to infinity. Therefore there are an infinitite number of points between you and the wall. It is impossible to "cross" infinity because then infinity is finite. So, you can never reach the wall.

But we do reach the wall. How is this possible?

There is no consensus on the matter.

Further, what does it mean to "touch" something? Is there something between you and the wall that you "touch"? (Physicists say yes)

Touching cannot be defined mathematically, but it is easily perceived.

These ideas lead some philosophers to claim that reality is only perception. I am because I am perceived. (I reach the wall and touch it, because I perceive it.)

Isn't our world, our lives, our minds and the present moment all just an amazing magical phenomenon?