论文部分内容阅读
当我们考察客观事物的数量关系或空间形式时,常常要断定它们是否具有某种属性,作出肯定或否定的回答。这种回答,就是数学中的判断。例如,下面四个句子,都是小学数学中的判断:(1)60°的角是锐角。(2)7只有两个约数。(3)X=3不是方程2x-1=7的解。(4)21不能被5整除。数学中的判断,有真有假,即有正确的,也有错误的。倘若一个判断如实地反映了客观事物的情况,那么这个判断就是真判断,即正确的判断;否则,这个判断就是假判断,即错误的判断。例如,(1)、(2)、(3)、(4)这四个判断,都是真判断;而“11是最小的二位教”,则是一个假判断。
When we look at the quantitative relations or spatial forms of objective things, we often decide whether they have certain attributes or not, and give affirmative or negative answers. This answer is the judgment in mathematics. For example, the following four sentences are all judgments in elementary mathematics: (1) The angle of 60 ° is acute. (2) 7 only two divisors. (3) X = 3 is not the solution of the equation 2x-1 = 7. (4) 21 can not be divisible by 5. Judgments in mathematics, true or false, that is correct, there are mistakes. If a judgment truthfully reflects the objective things, then this judgment is true judgment, that is, correct judgment; otherwise, this judgment is false judgment, that is, wrong judgment. For example, the four judgments of (1), (2), (3), and (4) are true judgments; and “11 is the smallest two-place teaching” is a false judgment.