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Does this contradiction Imply that distances smaller than a planck length do not exist, and that space is a discrete grid?

The same paradox occurs when considering photon energies. By measuring a photon's energy you are measuring its wavelength. Consider three photons, the first photon "A", has some arbitrary energy, the second photon "B", has a wavelength of half a planck length larger than the first photon, the third photon "C", has half a planck length larger still. The same effect applies to the energy of these three photons. If the planck length is the smallest measurable length then Photon "A" has indistinguishable energy from photon "B", which has indistinguishable energy from photon "C", but "A" and "C" are separated by a planck length, which will allegedly allow us to measure a difference in energy. Which is a paradox. Alternatively, If the planck length is the smallest measurable distance, then you might expect that all photon wavelengths occur in discrete multiples of the planck length. I don't really know, any ideas?