论文部分内容阅读
“數學學習”本年4月號第20頁所載“三個親密的朋友-0,1,∞”中有兩句話:“0可以看做∞的例數,∞可以看做0的例數”。我以為這兩句話不但容易使初學的人誤認為1/∞=0和1/0=∞,並且“∞的例數”和“0的例數”是沒有意義的。現在將有意義的0和∞看做沒有意義的東西,殊覺费解。舊書如葛斯郎三氏微積分中確乎有c/∞=0,c/0=∞這些樣的記法,雖然書中已談明這些是(?)的簡略形式,絕不是用∞或0去除常數c,但這兩種記法很容易引起不正確的觀念,還是應該批判的,又第22頁所載“一個小問題”的原文是:“如果以x-a除x的多項式f(x)
“Mathematics Learning” page 20 of this year’s “Three close friends - 0,1, ∞” contains two sentences: “0 can be regarded as the number of cases of ∞, and ∞ can be considered as the case of 0.” number". I think these two sentences are not only easy for beginners to mistakenly think that 1/∞=0 and 1/0=∞, and that the number of cases of “∞” and the number of cases of 0 are meaningless. Now it makes sense to think of meaningful 0 and ∞ as meaningless things. Old books such as Gossler’s three-dimensional calculus do indeed have c/∞=0, c/0=∞ such notations, although it is stated in the book that these are abbreviated forms of (?), never using ∞ or 0 to remove constants c. But these two types of notation can easily lead to incorrect concepts or should be criticized. The original text of “a small problem” on page 22 is: “If the polynomial f(x) is divided by xa