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Most investors associate minting non-fungible tokens (NFTs) with blockchain protocols like Solana and Ethereum.However, with the launch of its Ordinals protocol in January of 2023, Bitcoin (CRYPTO ...
Ordinals may be used to label the elements of any given well-ordered set (the smallest element being labelled 0, the one after that 1, the next one 2, "and so on"), and to measure the "length" of the whole set by the least ordinal that is not a label for an element of the set. This "length" is called the order type of the set.
In cryptocurrencies, an unspent transaction output (UTXO) is a distinctive element in a subset of digital currency models.A UTXO represents a certain amount of cryptocurrency that has been authorized by a sender and is available to be spent by a recipient.
The set C(α, β) is defined by induction on α to be the set of ordinals that can be generated from 0, ω 1, ω 2, ..., ω ω, together with the ordinals less than β by the operations of ordinal addition and the functions θ ξ for ξ<α. And the function θ γ is defined to be the function enumerating the ordinals δ with δ∉C(γ,δ). The ...
In 2023, ordinals—non-fungible tokens (NFTs)—on bitcoin, went live. [57] As of June 2023, River Financial estimated that bitcoin had 81.7 million users, about 1% of the global population. [58] In January 2024, the first 11 US spot bitcoin ETFs began trading, offering direct exposure to bitcoin for the first time on American stock exchanges.
The supremum of the ordinals that are the image of a function from ω ω (usually in models where the axiom of choice is not assumed) κ 1. Often used for a cardinal, especially the critical point of an elementary embedding 2. The Erdős cardinal κ(α) is the smallest cardinal such that κ(α) → (α) < ω λ 1. Often used for a cardinal 2.
Transfinite induction requires proving a base case (used for 0), a successor case (used for those ordinals which have a predecessor), and a limit case (used for ordinals which don't have a predecessor). Transfinite induction is an extension of mathematical induction to well-ordered sets, for example to sets of ordinal numbers or cardinal numbers.
In mathematics, even and odd ordinals extend the concept of parity from the natural numbers to the ordinal numbers. They are useful in some transfinite induction proofs. The literature contains a few equivalent definitions of the parity of an ordinal α: Every limit ordinal (including 0) is even. The successor of an even ordinal is odd, and ...