Ordinals

The word 'ordinal' means something far more interesting in set theory than in Bitcoin because ordinals are related to infinity. A set S with a linear ordering < is said to be well-ordered if every subset of S has a least element with respect to <. The well-ordering principle states that every set regardless of its size has a well-ordering. If S,T are well ordered sets, then either S and T are isomorphic as ordered sets or S is isomorphic to an initial segment of T or T is isomorphic to a proper initial segment of S. If two well ordered sets S,T are isomorphic, then we say that they have the same order type. If a well-ordered set S is isomorphic to an initial segment of a well-ordered set T, then we say that S has smaller order type of T. In set theory, we can define an ordinal to be an order type of some well-ordered set. But there are other ways of defining ordinals in set theory that have some advantages. For example, the way we have defined ordinals, the ordinals are equivalence classes rather than specific sets. In set theory, we can also define ordinals so that the ordinals are specific objects rather than equivalence classes.

The Bitcoin blockchain has attracted the brainless NFT dude bros naturally with its mining algorithm that was never designed to advance science. Since Bitcoin mining was never designed to advance science, it attracts people who hate science and reasoning. Bitcoin attracts anti-intellectuals. But it is not Bitcoin's fault. I blame organizations like the NIST along with the cryptography community because they have refused to standardize a cryptographic function that Bitcoin could have used to solve the most important scientific problem.

-Joseph Van Name Ph.D.

P.S. Multiply the ordinals (w^2*2+1)*(w*3+2). Beware. Ordinal addition and ordinal multiplication are non-commutative.