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如何證明1+1=2
試運用數學, 來證明1+1=2 更新: (我是有興趣知道)
最佳解答:
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 definition of addition to this: 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
其他解答:
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!|||||其實1+1唔一定=2，你聰明你知我講乜。|||||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.|||||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.html 2014-08-17 23:09:25 補充： http://www.tngs.tn.edu.tw/teaching/math/research/1%2B1=2.pdf 2014-08-17 23:27:24 補充： 某程度上， 1+1=2可以話係定義黎
如何證明1+1=2
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發問:試運用數學, 來證明1+1=2 更新: (我是有興趣知道)
最佳解答:
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 definition of addition to this: 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
其他解答:
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!|||||其實1+1唔一定=2，你聰明你知我講乜。|||||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.|||||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.html 2014-08-17 23:09:25 補充： http://www.tngs.tn.edu.tw/teaching/math/research/1%2B1=2.pdf 2014-08-17 23:27:24 補充： 某程度上， 1+1=2可以話係定義黎
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