英语翻译

题目

英语翻译
1、if there is a mapping of the natural numbers onto a set u(not necessarily one-to-one),then u is either finite or countable.
2、the existential-universal implies the universal-existential but not vice versa; the universal-existential is equivalent to asserting the existence of a function from the domain of the universally quantified variable to the domain of the existentially quantified variable.

答案

设有一个自然数集映射到一个集合U（不必是一一对映的）上,那么U要么是有限的,或者是可数的.
existential-universal的意思是universal-existential而不是相反,universal-existential等价于存在函数,其值域从universally quantified variable到existentially quantified variable
数学翻译啊,那几个专有名词不清楚对应哪个.