# 奥古斯塔斯·德摩根

## 维基百科，自由的百科全书

University College School

Frederick Guthrie

Francis Guthrie
Stephen Joseph Perry

## 生平

### 大学教育

1823年，16岁的他进入剑桥大学三一学院，与乔治·皮库克和威廉·修艾尔成为终身的好朋友。他受皮库克影响，引起了对代数和逻辑的兴趣。

## 思想

18世纪时仍有数学家怀疑负数的合法性，德摩根是其中的代表。德摩根自己在解代数方程时也会算出负数，但他认为当算出的答案为负数时，必需作特殊的说明，以回避负数本身的数学实在性。[2]德摩根使用负数和虚数，但他仍怀疑它们的数学意义。[3]他认为如果一个问题的最终答案算出来是负数，那说明原问题的提法不对。当算出最终答案为负数后，把原问题反过来提就可以保证答案为正数，困难就解决了。因此，他不认为负数一无是处，计算结果出现负数可以告诉解题者其问题的陈述方式搞反了。[1]

• 月球上的德摩根环形山

## 参考资料

1. Ralph A. Raimi. Augustus De Morgan and the Absurdity of Negative Numbers. University of Rochester. 1996年 （英语）. In his own time he was better known as a newspaper columnist...","'For example, 8-3 is easily understood; 3 can be taken from 8 and the remainder is 5; but 3-8 is an impossibility; it requires you to take from 3 more than there is in 3, which is absurd. If such an expression as 3-8 should be the answer to a problem, it would denote either that there was some absurdity inherent in the problem itself, or in the manner of putting it into an equation. Nevertheless, as such answers will occur, the student must be aware what sort of mistakes give rise to them, and in what manner they affect the process of investigation...'","... that his general idea, as we shall see, is that playing with absurdities like 3-8 AS IF they made sense can be made to lead to correct final conclusions.","'The principle is, that a negative solution indicates that the nature of the answer is the very reverse of that which it was supposed to be in the solution; for example, if the solution supposes a line measured in feet in one direction, a negative answer, such as -c, indicates that c feet must be measured in the opposite direction; if the answer was thought to be a number of days after a certain epoch, the solution shows that it is c days before that epoch; if we supposed that A was to receive a certain number of pounds, it denotes that he is to pay c pounds, and so on.'
2. ^ Negative Numbers. University of North Dakota. [2016年1月12日]. （原始内容存档于2016年2月11日） （英语）. Augustus de Morgan (1806-1871), an English mathematician, thought numbers less than zero were unimaginable.
3. ^ Daniel D. Merrill. Augustus De Morgan and the Logic of Relations. : 185–186.