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Sunday Math Party vol. 8 - Beyond Notation
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IWABUCHI Yu(u)ki butchi
January 07, 2017
Research
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150
Sunday Math Party vol. 8 - Beyond Notation
第8回 日曜数学会「記数法の彼方に」
記数法を研究を続けた結果、有限値より大きな値を表す記数法(いわば「無限進数」)は多項式の世界であることがわかりました。
IWABUCHI Yu(u)ki butchi
January 07, 2017
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Transcript
ه๏ͷ൴ํʹ ֶ༵ձ ؠ༐थ!CVUDIJ@Z
ࣗݾհ ؠ༐थ *8"#6$)*:V V LJ ۚେֶࣗવՊֶݚڀՊमྃ ത࢜ʢֶʣ
໘ന๏ਓΧϠοΫٕज़෦ɾਓࣄ෦ ଔݚͰಠࣗͷه๏ ʮஐʯΛݚڀ
ಥવͰ͕͢ʜ ͨ͢ʙʁ
ಥવͰ͕͢ʜ ͨ͢ʙʁ 2!
ಥવͰ͕͢ʜ ͨ͢ʙʁ 2!
ಥવͰ͕͢ʜ ͨ͢ʙʁ ∞
ϐμϋϯͷ ϐμϋϯ͕͢ϐμϋϯޠ ࣈʮʯʮʯ͔͠ͳ͍ ͦͷ࣍ʮ͍ͬͺ͍ʯ http://maru67bettencourt.blog82.fc2.com/blog-entry-1385.html
͓அΓ ʮ㱣ʯͱ͍͏දݱʹޠฐ͕͋ΔͷͰ ԾʹʮYʯͱஔ͖·͢ɻ
ਐʙ 㱣ͷੈքʙ ʹΛ͢ 1
ਐʙ 㱣ͷੈքʙ ɻ 1
ਐʙ 㱣ͷੈքʙ ʹΛ͢ 1
ਐʙ 㱣ͷੈքʙ ͜Εଘࡏ͠ͳ͍ 1
ਐʙ 㱣ͷੈքʙ Φʔόʔϑϩʔͯ͠ ͜͜ʹඈͿ 1 x
ਐʙ 㱣ͷੈքʙ Yɻ 1 x
ਐʙ 㱣ͷੈքʙ Y ɻ 1 x
ਐʙ 㱣ͷੈքʙ Φʔόʔϑϩʔ 1 x
ਐʙ 㱣ͷੈքʙ ·ͨΦʔόʔϑϩʔ 1 x x2
ਐʙ 㱣ͷੈքʙ Yɻ 1 x x2
ਐʙ 㱣ͷੈքʙ ͞Βʹ͢ͱ Y ɻ 1 x x2
ਐʙ 㱣ͷੈքʙ Y Y ͱ͍͑ɺ݁ہYͳͷͰɺ ͭ·Γ
ͱɺԽͰ͖Δ 1 x x2 x3 x4 x5
ਐʙ 㱣ͷੈքʙ ͔Βͷελʔτ 1
ਐʙ 㱣ͷੈքʙ ͤΔ 1
ਐʙ 㱣ͷੈքʙ ͤΔ 1
ਐʙ 㱣ͷੈքʙ ͤΔ 1
ਐʙ 㱣ͷੈքʙ Φʔόʔϑϩʔ 1 x
Ұؾʹඈ༂͠·͢ɻ
ແݶਐ ͷੈք ͑Εͳ͍ͱ͜ΖͰ Φʔόʔϑϩʔ 1 x めっちゃ 大きい数
͜͜ ͦ͏ɺه๏ͷ൴ํɻ
ແݶڃ ൺڃͷͭ ແݶྻΛ؆ܿͳࣜͰදͤΔʂ 1 x x2 x3 x4
x5
ΈࠐΈ FYY YY ࢉ͕ͦͷ··ΈࠐΈʹͳΔ ·͞ʹʮΈࠐΈੵʯ 1 x
x2 x3 x4 x5 1 x x2 x3 x4 x5 1 x x2 x3 x4 x5 × =
ඍ ඍੵࢉͰղܾ ͷܭࢉ͕ਖ਼͚͠Εɺ MPH Y ͷࢉ͕ඍɺ ͦͷٯͷࢉʢʹআࢉʣ͕ੵɻ
༑ਓʹ૬ஊ ʮ ɹ͋ΕɺͦΕʹࣅͨදݱํ๏Λ ɹͬͯΔʯ
ͦΕʮؔʯͩͬͨ ͓͓ɺఆٛ·Μ·͡ΌΜʂ
͜ͷຊʹࡌͬͯ·͢ ʢࠓ͖࣋ͬͯ·ͨ͠ʣ
͔͠͠ʜ ؔଟ߲ࣜͷYOಉ࢜ʹؔ࿈ੑ͕ ͋Δ͜ͱ͍ࣔࠦͯ͠ͳ͍ YOʹେখؔΛಋೖͰ͖Δ ֶతʹ۷ΓԼ͛ΔՁ͋Γʁ
ͦͦ ʮϋΠύʔϦϯΫʯͱ͍͏ࢥ ΑΓֶతʹࣗવͳ ܭࢉػΞʔΩςΫνϟʔΛߟ͑ͨɺ ࢥ͍͍ͭͨදݱ
ల ΦϒδΣΫτදه ৴߸ॲཧͷԠ༻ ܭࢉػͷݪཧͷԠ༻
͋͞ɺߦ͜͏ɻ ه๏ͷ൴ํʹ