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9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 99999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999998999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999 999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999 9999999999999999999999999999999999999999999999999999999999999999999999999999999999...もうやめていいですか?

数学的な性質[編集]

  • 1と等しい
  • 9を増やせば増やすほど1と等しくなる

1と等しいことの証明[編集]

1から0.999...を引くと0.000...と無限に続く数字の最後に1がつく数になる。

無限に続くのだから最後がなく、1をつける場所が無く、小数点以下の0を省略できる。

両辺に0.999...を足すとこうなり、証明ができた。

また、

0.999...=x

とすると、

2x=1.999...

となる。

2x-x=x

1.999...-0.999...=1

ということは、

x=1

8行上の式と重ねると、

x=1=0.999...

やはり、1=0.999...である。


もっと確実な証明が必要な頭の堅い方ウィキペディア0.999...へどうぞ。

0.999...を利用した計算式[編集]

1で済むのにわざわざ0.999...を使うバカはいねぇよ!しいて言えば

0.999...=1

だ!

0.999...の使い道[編集]

1を使えばいいだろ。というか、これを使用している人間は1と等しい事を知らないバカだけだろ……と言いたいところだが、一部で1を使用せずに0.999...を使用している例がある。

結婚式など
1は一桁で終わってしまうため、夫婦生活がすぐに終わってしまうことを連想させる。そのため、数学的に1と等しく、無限に桁がある0.999...が使用される。
余命など
例えば病院などで「余命1年でしょう」とか「1年もつか分かりません」と診断されると絶望的であるが「余命0.99999999...」と言えば無限に広がる夢が連想され、患者への精神的苦痛をおさえることができる。
ウィキペディアで使われている0.999...
0.999... - Wikipedia
何のためか分からないが、わざわざ右のような画像を使用してまで0.999...について説明しようとしている。まあ、このページも似たようなもんだが。
大学の数学

いちおー、大学の数学では0.999...は対角線論法という手法を通じて、自然数と実数の濃度(大きさのようなもの)が違うという証明をする際に使用する。0.999...を認めたくない学者は、この対角線論法をも攻撃する傾向がある。まったくもって、粘着質だ!ネチネチ。

0.999...を使えない場所・時[編集]

以下の場所・状況で1の代わりに0.999...を使用するとひよこ陛下に怒られ、殴られる。

葬式
0.999...は桁が無限に続く数字であるため、次々に死人が出ることや永遠に成仏できないことを連想させる。
1
ここでは1について説明しているため、0.999...は用無しである。ここの1を0.999...に置き換えると魔法使いに怒られるばかりでなく、アンサイクロペディアンとしての存在を抹消される。

0.999...の需要[編集]

上の計算式使い道を見ればわかるように、需要はほとんどなし。上記以外の使い方をしたきみは勇気の塊であり究極のバカだ!

覚え方[編集]

「れいてんくっくっくっくっくっくっ…」の語呂合わせを使えば簡単に覚えられる。

ちなみに、円周率は、小数第500億位ぐらいまで覚えるとギネスブックに載るけど、0.999...は、いくら先まで覚えてもギネスとして認定されない。これをギネス記録だと認めてくれる心の優しいネ申になる。

関連項目[編集]

Wikipedia
ユーモア欠落症患者のために、ウィキペディア専門家気取りたちが「0.999...」の項目を執筆しています。


数学書 この項目「0.999...」は、内容が足りません。このままでは驚くべき証明を書く余白が残ってしまいます。内容を充実させてくれる人を探しています。 (Portal:スタブ)