そーりー。じゃぱにーずおんりー。
ふと、思い出した（何を？）ので、マイナス×マイナスがプラスであることの説明を書いてみます。
説明 1 :
簡単なゲームを考えます。赤と青のカードがあって、2人で交互に山から取っていくゲームです。赤を取っても持ち点に変化はありません。青を引くと持ち点から5点引かれます。（なんてマイナス思考なゲームだ）
さて、あなたはこのゲームを行っていました。ゲームも終盤、残り4ターンの時点で、あなたと相手の点数は同じでした。その後の4ターンで相手は4回連続で赤を引き、あなたは4回連続で青を引いてしまいました。結果、あなたは相手に20点差を付けられて負けました。
そのとき、あなたは過去を振り返ってこう言うでしょう
「あぁ、4回連続で青なんか引かなければなぁ……」
さて、この言葉は、現時点よりも青を引いた回数が4回少なかったら負けて無かったということを意味しています。つまり、-5点のカードを引いた回数が今と比べて-4回だった場合、点数は今よりも+20点だったということです。つまり
(-5) × (-4) = 20
と言ったのです。オシマイ。
説明 2 :
正の数(実数) a と b を考える。
(-a) × (-b) = ab
であることを示したい。
[マイナスの定義]
(-a) は a + (-a) = 0 となる数。
[1の定義]
1とは 1a = a となる数。
ここで、分配法則を利用して
a + (-1)a = 1a + (-1)a = (1+(-1))a = 0
[0の定義]
0とは 0 + a = a + 0 = a となる数なので
(-1)a = (-1)a + 0 = (-1)a + a + (-a) = 0 + (-a) = (-a)
となる。よって(-1)a = (-a)
以上より
(-a) × (-b) = (-1)a × (-1)b
交換法則より
(-1)a × (-1)b = (-1)(-1)ab
ここで、
(-1)(-1) は (-1)a = -a と同じようにして (-1)(-1) = -(-1) とできる。
さらに、-(-x)は
(-x) + (-(-x)) = 0
となる数なので
x = x + 0 = x + (-x) + (-(-x)) = 0 + -(-x) = -(-x)
よって、x = 1のとき、 -(-1) = 1
従って、
(-1)(-1)ab = 1×ab = ab
以上より
(-a) × (-b) = ab
……あってる？
(2)はともかく、(1)のようなたとえ話をするときは、「過去を振り返る」とか、「あるはずのもの（あった方が良いもの）が無い」という小細工を話に含めないと上手くいかないです。どうにかならないかなぁ。
http://gorimutyu.net/cgi-bin/mt/mt-tb.cgi/193
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