Chapter 24 <Empty wine bottle equals full wine bottle>

Xiao Zhao, Xiao Qian, Xiao Sun, and Xiao Li are classmates, and they often get together to discuss problems.One day, the four of them had dinner at the same table and argued over the half bottle of wine on the table. Xiao Zhao said: This bottle is half empty. Xiaoqian said: This bottle is half full. Xiao Sun said: There is no arguing about it, a half-empty wine bottle is equal to a half-full wine bottle. Xiao Li said: No.If the equation that a half-empty bottle equals a half-full bottle holds true, then we multiply both sides of the equation by two: a half-empty bottle multiplied by two equals two half-empty bottles, and two half-empty bottles is one An empty bottle; a half-full bottle multiplied by two equals two half-full bottles, and two half-full bottles is one full bottle.So, is not an empty wine bottle equal to a full wine bottle?

Xiao Sun's words made the mistake of subverting concepts. In fact, the relationship between the half-empty wine bottle and the half-full wine bottle is a mutual implication relationship, or a relationship that can be deduced from each other, that is, it can be deduced from the half-empty wine bottle that it is a half-full wine bottle, and vice versa. , also the same.However, Xiao Sun used the concept of equal to secretly replace the concept of derivability, which is wrong, because half empty is different from half full.This is like knowing that half of the twenty students in a certain class are boys and the other half are girls. We can deduce the latter from the former, or the former from the latter, but we cannot say that ten boys equal ten girls.

Xiao Li pointed out that Xiao Sun's words were wrong, which is correct.But Xiao Li also made the mistake of subverting concepts in his rebuttal.It manifests itself in the fact that he thinks that two half-empty bottles are an empty bottle and two half-full bottles are a full bottle.Since two half-empty bottles and two half-full bottles clearly mean two bottles, how can they be one bottle?That is, two half-empty bottles are not one empty bottle, and two half-full bottles are not one full bottle. Xiao Li's sophistry mistake was to secretly replace two wine bottles with one wine bottle.