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Okay, I asked this in one of the previous threads, but I can't remember the answer.
Bottle caps increase the stats of a Pokemon to the point at which they were as if the Pokemon had a perfect 31 IVs in each stat. However, Bottle Caps don't raise the actual IV, leaving inheritance and Hidden Power's type unaffected.
Also, Regardless of a Pokemon's EVs or IVs, a stat benefiting from a nature will always have a higher limit than the stat of a Pokemon with a neutral nature.
Therefore, if one has enough patience to raise a Pokemon to level 100 and enough Bottle Caps, they only need to breed for a beneficial nature, egg moves, and shininess, correct?