Re: [轉錄][新聞] 30÷2(2+3)÷5是多少？　計算機딠…

看板Math作者childwen (呵呵)時間14年前 (2011/04/13 14:57)推噓13(13推 0噓 15→)

留言28則, 12人參與討論串27/48 (看更多)

※ 引述《jeffonett (Taiwan 加油!)》之銘言： : ‧這種沒定義的情況,除非數學協會給個定義, : 不能說純數式(一般計算式)or代數式哪個一定不對. : ‧電子計算機的邏輯為人腦所寫,若不夠嚴謹就會出包. : ‧若一定要說有唯一解, 請附美國數學協會的公文或定義. : ‧沒有乘號是從代數發跡,代數思維的命題,用代數思維解題較嚴謹. : (如同高中數學/物理你要考慮的參數比國小更多) : ‧沒有定義的情況下,兩種答案都是對的,用這2種轉換式邏輯上都可以接受. : ‧/號請定義為"分號(紙本運算子)"或是"÷號(電腦運算子)". 我同意jeffonett說的這題目本身定義不清前面有版友提出一個連結(太多篇我忘了是哪篇XD) http://mathforum.org/library/drmath/view/54341.html 提出的問題是 ax/by = ? (1) (a*x/b)*y (2) (a*x)/(b*y) [15派] [0.6派] 回答的是Doctor Peterson 不知道是誰但他的說法蠻能讓我接受的他說他偏向第1種做法在沒有特別說明下就是由左至右計算但有些教科書上會明文寫出「當乘號省略時此乘法優先於所有計算」也就是採用第2種做法但這並非一個general rule 因此在未說明的情況下就擅用第2種做法是不太正確的以下這段寫的很好 So to answer your question, I think both answers can be considered right - which means, of course, that the question itself is wrong. I prefer the standard way (your first answer) when talking to students, unless their own text gives the "implicit multiplication first" rule; but in practice if I came across that expression, I would probably first check where it came from to see if I could tell what was intended. The main lesson to learn is not which rule to follow, but how to avoid ambiguity in what you write yourself. Don't give other people this kind of trouble. 簡而言之題意不清兩個答案都可視為正確別被"遵循哪個rule"而困住了重點是避免像這樣模稜兩可的表示法大家有求知的態度很好但當題意不清時就別執著於找出唯一解啦附上同個網站關於typing math的說明 http://mathforum.org/dr.math/faq/faq.typing.math.html 可以看一下中間Fractions的部分 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 114.38.69.98

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jeffonett

04/13 15:00, , 1^F

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ricestone

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zson

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這個連結中有人提到 One convention from the American Mathematical Society is this one: "multiplication indicated by juxtaposition is carried out before division." 我不知道這句話的真實性但又連結到跟原文同一個網站的另一篇文 http://mathforum.org/library/drmath/view/57021.html 問問題的是電工的教授他提到上述這個convention來自 Mathematical Reviews Database - Guide for Reviewers http://www.ams.org/authors/guide-reviewers.html 但連結已失效無從查證 (有人知道怎麼查詢嗎?請幫忙) 回答者同樣為Doctor Peterson the fact that they took note of this one rule alone demonstrates only that this is the one rule on which there is not universal agreement at the present time, but it probably is growing in acceptance. 就是說「乘號省略時的乘法優先算」並不是一個世界通用的規則雖然這樣的概念已越來越被接受所以我們能做的 1.避免符號運用的混淆該加括號時就別客氣 2.要求AMS訂出通用規則

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gwendless

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zson

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zson

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