Zen personal trouble or crisis. Though Zen-narrative states that it is a "special transmission outside scriptures" which "did not stand upon words", Zen does have a rich doctrinal background, which is firmly grounded in the Buddhist tradition. It was thoroughly influenced by the Chinese understanding of Yogacara and the Buddha-nature doctrine, Zen integrates both Yogacara and Madhyamaka and the influence of Madhyamaka can be discerned in the stress on non-conceptual insight and the paradoxical language of the koans. Most essential are "the most fundamental teaching that we are already originally enlightened", and the Bodhisattva ideal, which supplements insight with Karuṇā, compassion
Paradoxical set Paradoxical set In set theory, a paradoxical set is a set that has a paradoxical decomposition. A paradoxical decomposition of a set is two families of disjoint subsets, along with appropriate group actions that act on some universe (of which the set in question is a subset), such that each partition can be mapped back onto the entire set using only finitely many distinct functions (or compositions thereof) to accomplish the mapping. A set that admits such a paradoxical decomposition where the actions belong to a group formula_1 is called formula_1-paradoxical or paradoxical with respect to formula_1. Paradoxical sets exist