Yahoo 知識+ 將於 2021 年 5 月 4 日 (美國東岸時間) 停止服務。從 2021 年 4 月 20 日 (美國東岸時間) 起，Yahoo 知識+ 網站將轉為僅限瀏覽模式。其他 Yahoo 資產或服務，或你的 Yahoo 帳戶將不會有任何變更。你可以在此服務中心網頁進一步了解 Yahoo 知識+ 停止服務的事宜，以及了解如何下載你的資料。

trees
Lv 4
trees 發問於 科學及數學數學 · 7 年前

# 如何證明1+1=2

(我是有興趣知道)

### 6 個解答

• 7 年前
最愛解答

Proof that 1 + 1 = 2

Date: 06/10/99 at 00:03:59

From: mike

Subject: Need the math proof for 1 + 1 = 2

My wife the math teacher wants the mathematical proof for

1 + 1 = 2

I have spent quite a bit of time looking for it on the Web - help!

Date: 06/10/99 at 10:15:58

From: Doctor Rob

Subject: Re: Need the math proof for 1 + 1 = 2

The proof starts from the Peano Postulates, which define the natural

numbers N. N is the smallest set satisfying these postulates:

P1. 1 is in N.

P2. If x is in N, then its "successor" x' is in N.

P3. There is no x such that x' = 1.

P4. If x isn't 1, then there is a y in N such that y' = x.

P5. If S is a subset of N, 1 is in S, and the implication

(x in S => x' in S) holds, then S = N.

Then you have to define addition recursively:

Def: Let a and b be in N. If b = 1, then define a + b = a'

(using P1 and P2). If b isn't 1, then let c' = b, with c in N

(using P4), and define a + b = (a + c)'.

Then you have to define 2:

Def: 2 = 1'

2 is in N by P1, P2, and the definition of 2.

Theorem: 1 + 1 = 2

Proof: Use the first part of the definition of + with a = b = 1.

Then 1 + 1 = 1' = 2 Q.E.D.

Note: There is an alternate formulation of the Peano Postulates which

replaces 1 with 0 in P1, P3, P4, and P5. Then you have to change the

Def: Let a and b be in N. If b = 0, then define a + b = a.

If b isn't 0, then let c' = b, with c in N, and define

a + b = (a + c)'.

You also have to define 1 = 0', and 2 = 1'. Then the proof of the

Theorem above is a little different:

Proof: Use the second part of the definition of + first:

1 + 1 = (1 + 0)'

Now use the first part of the definition of + on the sum in

parentheses: 1 + 1 = (1)' = 1' = 2 Q.E.D.

- Doctor Rob, The Math Forum

2014-08-18 07:47:31 補充：

畫圈圈來表示:

o+o=oo

• ?
Lv 7
7 年前

對! 单是出題 1+1 = 2 係未完全的.祇係一般當佢十進制啫.

其實在二進制係=10.....(電腦, 計算機, 太空科學, 導弹,衛星等等, 都係二進制)

尚有三進制,四進進制....等等.

就如在某一地方, 問你一蚊買到幾多野一樣, 美金同港纸就差一大截!

• ?
Lv 7
7 年前

其實1+1唔一定=2，你聰明你知我講乜。

• 7 年前

I know that everyone of you are interesting in proving 1+1=2, but, as a professional and an experienced teacher in mathematics, I must tell you the proving is quiet challenging that it does not work by yourself as you are a student or do not very get familarise in all those mathematic area. In fact, the proving of 1+1=2 combines of several topics like trigonometry, calculus, and so on, simply say you cannot attain this proving at the moment.

資料來源： RUBBISH
• 你覺得這個解答怎樣？你可以登入投選解答。
• 7 年前

呢條問題唔係第一次有人問。

每次都可以反問問的人，你如何定義「２」？

2014-08-17 23:18:49 補充：

如果問的人無法定義２，即是題目也不成立，那任憑你用什麼方法去所謂「證明」都是徒勞無功。

都是等發問者告訴清楚以下的定義：

✿ 1 這個數字的意思

✿ 2 這個數字的意思

✿ + 這個符號的意思

✿ = 這個符號的意思

然後才回答吧。

• http://mathforum.org/library/drmath/view/51551.htm...

2014-08-17 23:09:25 補充：

http://www.tngs.tn.edu.tw/teaching/math/research/1...

2014-08-17 23:27:24 補充：

某程度上，

1+1=2可以話係定義黎