为什么零不能做除数？
Why can't zero be a divisor?
除法是乘法的逆运算：a/b 要找 x 使 b·x = a。b 换成 0，这条路就断了，任何数乘 0 仍是 0，a 不为 0 时无解，a 也是 0 时任何 x 都行，两头都得不出唯一的商，只能判为无定义。它也不是无穷大：除数越接近 0 商越大只是趋势，如 1 除以 0.001 得 1000，而 0 并不是一个可取的除数。
Division is the inverse of multiplication: a/b asks for an x with b·x = a. Set b to 0 and that route breaks, because any number times 0 is still 0; if a is not 0 there is no solution, and if a is 0 as well every x works. Neither case yields a unique quotient, so the operation is undefined. It is not infinity either: the quotient growing as the divisor nears 0 is only a trend, and 1 divided by 0.001 gives 1000, yet 0 is not a divisor one may take.
来源 · Source
Courant & Robbins,《What Is Mathematics?》Oxford University Press,1996 第二版;中译《什么是数学》
R. Courant and H. Robbins, What Is Mathematics?, Oxford University Press, 1996; Chinese ed.
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