[過去ﾛｸﾞ] 純粋・応用数学・数学隣接分野（含むガロア理論）15 (1002ﾚｽ)
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572(3): 2023/08/15(火)23:48 ID:TPe4RI1p(17/17) AAS
>>568
>there is a method of predicting the value f(a) of a function f mapping the reals to the reals, based only on knowledge of f's values on the open interval (a – 1, a)
>とありますけど？
なるほど
ありがとう
これ、謎のプロ数学者氏が好きそうな話題かもねｗ
えーと>>560より、関連含め引用下記
This book deals with the question of how successfully one can predict the value of an arbitrary function at one or more points of its domain based on some knowledge of its values at other points.
Topics range from hat problems that are accessible to everyone willing to think hard, to some advanced topics in set theory and infinitary combinatorics.
For example, there is a method of predicting the value f(a) of a function f mapping the reals to the reals, based only on knowledge of f's values on the open interval (a – 1, a), and for every such function the prediction is incorrect only on a countable set that is nowhere dense.
省13
573: 2023/08/16(水)02:56 ID:eVupkbff(1/6) AAS
>>572
>４）もし、fが連続関数ならば、極限を使って、下からaに近づくようにして
> lim x→a {f(x)} とすれば、 f(x)→f(a)ですよね？
ダメです。
なぜなら
This book deals with the question of how successfully one can predict the value of an arbitrary function at one or more points of its domain based on some knowledge of its values at other points.
とある通り、対象が arbitrary function だから。
>５）「予測が正しくないのは、密度がどこも稠密でない可算集合の場合のみ」
> この意味は、開区間 (a – 1, a)の関数値の情報が、"稠密でない可算集合"つまり、離散値と解せられます
違います。
省10
583: 新 現代数学の系譜 雑談 ◆yH25M02vWFhP 2023/08/16(水)13:02 ID:VDPkTO11(1/3) AAS
>>572 追加
>>560より
外部ﾘﾝｸ[html]:books.google.co.jp
ここで、内部を検索で、キーワード predict
で、下記2件 ヒット
vii ページ
This book deals with the question of how successfully one can predict the value of an arbitrary function at one or more ... For example, there is a method of predicting the value f.a/ of a function f mapping the reals to the reals, ...
8 ページ
In Chap.7 we start to move further away from the hat problem metaphor and think instead of trying to predict a function's value at a point based on knowing (something about) its values on nearby points ...
そして 560-561より
省7
598: 2023/08/16(水)23:42 ID:mCsbmoTJ(2/4) AAS
>>572 追加
まず訂正
２）開区間 (a – 1, a)上の連続濃度の関数値 f(a-1)〜f(a)が知られている
↓
２）開区間 (a – 1, a)上の連続濃度の関数値 f(a-1)〜f(a')が知られている(但しa'<a)
<本題>
(引用開始)
For example, there is a method of predicting the value f(a) of a function f mapping the reals to the reals, based only on knowledge of f's values on the open interval (a – 1, a), and for every such function the prediction is incorrect only on a countable set that is nowhere dense.
ですね
＜google訳(一部手直し)＞
省6
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