(参考) https://ja.wikipedia.org/wiki/0%E3%81%AE0%E4%B9%97 0の0乗 (抜粋) 0 の 0 乗(ゼロのゼロじょう、英: zero to the power of zero, 0 to the 0th power)は、累乗あるいは指数関数において、底を 0、指数を 0 としたものである。その値は、代数学、組合せ論、集合論などの文脈ではしばしば 1 と定義される[注 1]一方で、解析学の文脈では二変数関数 xy が原点 (x, y) = (0, 0) において連続とならないため定義されない場合が多い。
(参考) https://en.wikipedia.org/wiki/Zero_to_the_power_of_zero Zero to the power of zero (抜粋) Zero to the power of zero, denoted by 0^0, is a mathematical expression with no agreed-upon value. The most common possibilities are 1 or leaving the expression undefined, with justifications existing for each, depending on context. In algebra and combinatorics, the generally agreed upon value is 0^0 = 1, whereas in mathematical analysis, the expression is sometimes left undefined. Computer programs also have differing ways of handling this expression.
History of differing points of view The debate over the definition of 0^0 has been going on at least since the early 19th century. At that time, most mathematicians agreed that 0^0=1, until in 1821 Cauchy[13] listed 0^0 along with expressions like 0/0 in a table of indeterminate forms. In the 1830s Guglielmo Libri Carucci dalla Sommaja[14][15] published an unconvincing argument for 0^0=1, and Mobius[16] sided with him, erroneously claiming that lim t → 0^+ f(t)^g(t) = 1 whenever lim t → 0^+ f(t)= lim t → 0^+ g(t)= 0 . A commentator who signed his name simply as "S" provided the counterexample of (e^{-1/t )^t , and this quieted the debate for some time.
つづき More historical details can be found in Knuth (1992).[17]
More recent authors interpret the situation above in different ways: ・Some argue that the best value for 0^0 depends on context, and hence that defining it once and for all is problematic.[18] According to Benson (1999), "The choice whether to define 0^0 is based on convenience, not on correctness. If we refrain from defining 0^0, then certain assertions become unnecessarily awkward. [...] The consensus is to use the definition 0^0=1 0^0=1, although there are textbooks that refrain from defining 0^0."[19]
・Others argue that 0^0 should be defined as 1. Knuth (1992) contends strongly that 0^0 "has to be 1", drawing a distinction between the value 0^0, which should equal 1 as advocated by Libri, and the limiting form (an abbreviation for a limit of f(x)^g(x) where f(x),g(x) → 0 ), which is necessarily an indeterminate form as listed by Cauchy : "Both Cauchy and Libri were right, but Libri and his defenders did not understand why truth was on their side."[17] Vaughn gives several other examples of theorems whose (simplest) statements require 0^0 = 1 as a convention.[20] (引用終り) 以上 0401現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/14(火) 11:37:48.47ID:PFls8jJA>>400 タイポ訂正
The consensus is to use the definition 0^0=1 0^0=1, although there are textbooks that refrain from defining 0^0."[19] ↓ The consensus is to use the definition 0^0=1, although there are textbooks that refrain from defining 0^0."[19] 0402132人目の素数さん2020/08/21(金) 23:22:17.78ID:RM9y96NI>>3 それ結構深い比喩かもとちょっと思った 0403132人目の素数さん2020/08/21(金) 23:23:57.06ID:RM9y96NI>>20 いやいや背理法だよ 0404132人目の素数さん2020/09/09(水) 22:58:19.73ID:IR7822fG とんでも数学 0405青戸六丁目被害者の会(本部:葛飾区青戸6−26−6)2021/03/09(火) 20:27:49.78ID:5gIZP/7W ●青戸六丁目被害者住民一同「色川高志の金属バット集団殴打撲殺を熱望します」 長木親父&長木よしあき(盗聴盗撮犯罪者の色川高志を逮捕に追い込む会&被害者の会会長)住所=東京都葛飾区青戸6−23−20 ●龍神連合五代目総長・色川高志(葛飾区青戸6−23−21ハイツニュー青戸103)の挑発 色川高志「糞関東連合文句があったらいつでも俺様を金属バットで殴り殺しに来やがれっ!! 糞関東連合の見立・石元・伊藤リオンの糞野郎どもは 龍神連合五代目総長の俺様がぶちのめしてやるぜっ!! 賞金をやるからいつでもかかって来いっ!! 糞バエ関東連合どもっ!! 待ってるぜっ!!」(挑戦状)