Yes, there is a bijective mapping between the set of natural numbers and the set of all binary tree shapes. This result is known as "Cayley's theorem," named after the British mathematician Arthur Cayley, who first stated it in 1889. According to the theorem, there is a bijection between the set of labeled trees (binary or otherwise) on n nodes and the set of elements of the symmetric group S_n.
spam fails_task lang_mismatch pii not_appropriate hate_speech sexual_content quality toxicity humor helpfulness creativity violence