Hash Tables Lead To Fast Searches

The hash table of the set {x₁, x₂, x₃, ...} is the set {(H(x₁), x₁), (H(x₂), x₂), (H(x₃), x₃), ...} for some hash function H.  Hash tables are used to implement dictionaries where the vector portions hashed are the keys.  Consider storing the hash tables of sets in memory and using the hashes for memory addresses.  Then, searching the sets would then mainly involve finding hashes!