You actually cannot divide a distance infinitely. There is a smallest unit of length, the Planck Length. You cannot subdivide the Planck Length. Thus there is a finite number of Planck Lengths between any two points. There is not an infinite subdivision of anything.
You cannot even subdivide time infinitely. There is a smallest unit of time that has any meaning, the Planck time. Anything smaller than that would be so unstable, so variable due to quantum fluctuations, as to make that 'thing' spontaneously change in position or time by an amplitude equal to the Planck length or Planck time (which is why these are the minimal units). That is, there is no absolute 'stillness' or 'present'. There is only position that varies at least by a variation equal to the Planck length, and only a moment in time that is at least as variable as one Planck unit of time. Zeno's paradox is a dead issue. 1 centimeter equals 6.1873559 × 10^32 Planck Lengths. One second equals 1.855094832e+43 Planck time units.
Infinity is itself just an abstract concept. No actual infinities can exist. And even the thought experiment of dividing distance over and over again by halving your distance to the wall, taking a step, halving that distance, taking a step, halving that step and so on... even that fails because you cannot keep this up forever. You eventually will be One Planck unit away from the wall and won't be able to get any closer because the wall itself varies in position by at least one planck unit constantly. Given repulsion effects of atoms dominate at many times larger than a Planck unit, you won't be able to get closer than the orbits of the electrons of the molecules of the wall and those of your body. Rather, the magnetic repulsion of your electron shells on the surface of your body and that of the wall will dominate well before you get to even that distance.
But as a though experiment, we need to recognize that the universe we live in does abide by the rules of quantum mechanics. Reality is the reference frame for even our thought experiments. As such, you cannot have a paradox of subdivision like the one called Zeno's paradox. Given there is a minimal time or distance that has any meaning, there can be no actual infinities of any property defined in space or time.