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  1. 私は この 解剖学 的な 知識を オーディナルズの アート に 注ぎ込んだ.
    #Ordinals #Digitalartifacts #Digitalassets #Web3D

  2. わたしは えいえん に あなたの よろこびの ために じょすうしの ごいの なか に みを ささげ ます.
    #Ordinals #Digitalartifacts #Digitalassets #Web3

  3. わたしは あなたの ために えいえん に ウェブ 3ひろさ に みを ささげ ます.

    #Ordinals #Digitalartifacts #Digitalassets #Web3

  4. おはようございます うつくしい こうたくの ある。☀️
    #Ordinals #Digitalartifacts #Digitalassets #Web3

  5. ビットコイン ブロックチェーンからの おんしゃ に かんしゃ しています。🙏

    #Ordinals #Digitalartifacts #Digitalassets #Web3

  6. ゆたか な せいかつ と しゅくふくを ありがとうございます。
    #Ordinals #Digitalartifacts #Digitalassets #Web3

  7. わたしを しゅくふく して くれる すべての しゅんかんに かんしゃ します。
    #ordinals #digitalartifacts #digitalassets #web3

  8. Every well-ordered set is isomorphic to an ordinal. Common notion, for example see Introduction to arxiv.org/abs/2409.07352

    ⊢((𝐴∈V∧𝑅We𝐴)↔∃𝑓(dom𝑓∈On∧𝑓IsomE,𝑅(dom𝑓,𝐴)))

    \[ \vdash ( ( A \in \mathrm{V} \wedge R \mathrm{We} A ) \leftrightarrow \exists f ( \mathrm{dom} f \in \mathrm{On} \wedge f \mathrm{Isom} \mathrm{E} , R ( \mathrm{dom} f , A ) ) ) \]

    Every well-ordered set is isomorphic to
    a unique ordinal.

    ⊢((𝐴∈V∧𝑅We𝐴)↔∃!𝑜∈On∃𝑓∈(𝐴↑ₘ𝑜)𝑓IsomE,𝑅(𝑜,𝐴))

    \[ \vdash ( ( A \in \mathrm{V} \wedge R \mathrm{We} A ) \leftrightarrow \exists{!} o \in \mathrm{On} \exists f \in ( A \uparrow_\mathrm{m} o ) f \mathrm{Isom} \mathrm{E} , R ( o , A ) ) \]

    We can phrase the Axiom of Choice as "Every set injects into an ordinal."

    ⊢(CHOICE↔∀𝑥∃𝑜∈On𝑥≼𝑜)

    \[ \vdash ( \mathrm{CHOICE} \leftrightarrow \forall x \exists o \in \mathrm{On} x \preccurlyeq o ) \]

    #math #metamath #SetTheory #WellOrdering #OrdinalNumbers

  9. Every well-ordered set is isomorphic to an ordinal. Common notion, for example see Introduction to arxiv.org/abs/2409.07352

    ⊢((𝐴∈V∧𝑅We𝐴)↔∃𝑓(dom𝑓∈On∧𝑓IsomE,𝑅(dom𝑓,𝐴)))

    \[ \vdash ( ( A \in \mathrm{V} \wedge R \mathrm{We} A ) \leftrightarrow \exists f ( \mathrm{dom} f \in \mathrm{On} \wedge f \mathrm{Isom} \mathrm{E} , R ( \mathrm{dom} f , A ) ) ) \]

    Every well-ordered set is isomorphic to
    a unique ordinal.

    ⊢((𝐴∈V∧𝑅We𝐴)↔∃!𝑜∈On∃𝑓∈(𝐴↑ₘ𝑜)𝑓IsomE,𝑅(𝑜,𝐴))

    \[ \vdash ( ( A \in \mathrm{V} \wedge R \mathrm{We} A ) \leftrightarrow \exists{!} o \in \mathrm{On} \exists f \in ( A \uparrow_\mathrm{m} o ) f \mathrm{Isom} \mathrm{E} , R ( o , A ) ) \]

    We can phrase the Axiom of Choice as "Every set injects into an ordinal."

    ⊢(CHOICE↔∀𝑥∃𝑜∈On𝑥≼𝑜)

    \[ \vdash ( \mathrm{CHOICE} \leftrightarrow \forall x \exists o \in \mathrm{On} x \preccurlyeq o ) \]

    #math #metamath #SetTheory #WellOrdering #OrdinalNumbers

  10. Every well-ordered set is isomorphic to an ordinal. Common notion, for example see Introduction to arxiv.org/abs/2409.07352

    ⊢((𝐴∈V∧𝑅We𝐴)↔∃𝑓(dom𝑓∈On∧𝑓IsomE,𝑅(dom𝑓,𝐴)))

    \[ \vdash ( ( A \in \mathrm{V} \wedge R \mathrm{We} A ) \leftrightarrow \exists f ( \mathrm{dom} f \in \mathrm{On} \wedge f \mathrm{Isom} \mathrm{E} , R ( \mathrm{dom} f , A ) ) ) \]

    Every well-ordered set is isomorphic to
    a unique ordinal.

    ⊢((𝐴∈V∧𝑅We𝐴)↔∃!𝑜∈On∃𝑓∈(𝐴↑ₘ𝑜)𝑓IsomE,𝑅(𝑜,𝐴))

    \[ \vdash ( ( A \in \mathrm{V} \wedge R \mathrm{We} A ) \leftrightarrow \exists{!} o \in \mathrm{On} \exists f \in ( A \uparrow_\mathrm{m} o ) f \mathrm{Isom} \mathrm{E} , R ( o , A ) ) \]

    We can phrase the Axiom of Choice as "Every set injects into an ordinal."

    ⊢(CHOICE↔∀𝑥∃𝑜∈On𝑥≼𝑜)

    \[ \vdash ( \mathrm{CHOICE} \leftrightarrow \forall x \exists o \in \mathrm{On} x \preccurlyeq o ) \]

    #math #metamath #SetTheory #WellOrdering #OrdinalNumbers

  11. Ordinals e o problema dos UTXOs

    Você sabia que a implementação dos Ordinals em 2023 tornou muito mais difícil rodar um nó Bitcoin em dispositivos fracos? 🤯

    • O problema:
    - Crescimento exponencial de UTXOs de 1 satoshi com a chegada dos Ordinals.

    • Consequência:
    - Máquinas de baixo poder (ex: Raspberry Pi) passaram a não conseguir validar o blockchain inteiro sincronizando do zero.

    • Solução prática (workaround):
    - Valide...

    #Bitcoin #Blockchain #Ordinals #UTXOs #RaspberryPi #MorningCrypto

  12. Ordinals e o problema dos UTXOs

    Você sabia que a implementação dos Ordinals em 2023 tornou muito mais difícil rodar um nó Bitcoin em dispositivos fracos? 🤯

    • O problema:
    - Crescimento exponencial de UTXOs de 1 satoshi com a chegada dos Ordinals.

    • Consequência:
    - Máquinas de baixo poder (ex: Raspberry Pi) passaram a não conseguir validar o blockchain inteiro sincronizando do zero.

    • Solução prática (workaround):
    - Valide...

    #Bitcoin #Blockchain #Ordinals #UTXOs #RaspberryPi #MorningCrypto

  13. Ordinals e o problema dos UTXOs

    Você sabia que a implementação dos Ordinals em 2023 tornou muito mais difícil rodar um nó Bitcoin em dispositivos fracos? 🤯

    • O problema:
    - Crescimento exponencial de UTXOs de 1 satoshi com a chegada dos Ordinals.

    • Consequência:
    - Máquinas de baixo poder (ex: Raspberry Pi) passaram a não conseguir validar o blockchain inteiro sincronizando do zero.

    • Solução prática (workaround):
    - Valide...

    #Bitcoin #Blockchain #Ordinals #UTXOs #RaspberryPi #MorningCrypto

  14. RE: mas.to/@ordinal/11602007616132

    One thing about this setting is that it must clearly have groats. I think #wfrp missed a trick with the lack of coinage between penny and shilling.

  15. RE: mas.to/@ordinal/11602007616132

    One thing about this setting is that it must clearly have groats. I think #wfrp missed a trick with the lack of coinage between penny and shilling.

  16. RE: mas.to/@ordinal/11602007616132

    One thing about this setting is that it must clearly have groats. I think #wfrp missed a trick with the lack of coinage between penny and shilling.

  17. RE: mas.to/@ordinal/11602007616132

    One thing about this setting is that it must clearly have groats. I think missed a trick with the lack of coinage between penny and shilling.

  18. Bitcoin DeFi is splitting into two designs: indexer-embedded VMs vs. Decentralized PSBT Signing. We compare MEV, latency, UX, and more... hackernoon.com/what-the-battle #ordinals

  19. Bitcoin DeFi is splitting into two designs: indexer-embedded VMs vs. Decentralized PSBT Signing. We compare MEV, latency, UX, and more... hackernoon.com/what-the-battle #ordinals

  20. Bitcoin DeFi is splitting into two designs: indexer-embedded VMs vs. Decentralized PSBT Signing. We compare MEV, latency, UX, and more... hackernoon.com/what-the-battle #ordinals

  21. Bitcoin DeFi is splitting into two designs: indexer-embedded VMs vs. Decentralized PSBT Signing. We compare MEV, latency, UX, and more... hackernoon.com/what-the-battle

  22. Bitcoin DeFi is splitting into two designs: indexer-embedded VMs vs. Decentralized PSBT Signing. We compare MEV, latency, UX, and more... hackernoon.com/what-the-battle #ordinals

  23. BitMEX Research Report Flags BRC-20 as the Real Strain on Bitcoin Nodes - In a newly published report, BitMEX Research and its analysts say BRC-20 activity,... - news.bitcoin.com/bitmex-resear #ordinalinscriptions #bitcoin(btc) #cryptonews