I have a confusion in mind that since in hashing we transform a large string into a smaller fixed size string, so its unlikely that any large string has a unique hash. There had to be collisions and repetition since the number of bits are reduced and mathematically it seems unlikely that smaller number of bits represent a large number of bits with uniqueness.
For guaranteed uniqueness its only possible if the input bits is equal to output bits.
Not having a possibility to find a pre-image is a different thing, my question is about the existence of a pre-image, whether it should exist or not? I think it should always exist.