SOLOVARY proved that every regular uncountable κ is the union of κ disjoint stationary sets (ref. [1], Theorem 85). Let κ be an ineffable ordinal, and let A(?)κ. If A is an ineffable set, then A is a stationary se...SOLOVARY proved that every regular uncountable κ is the union of κ disjoint stationary sets (ref. [1], Theorem 85). Let κ be an ineffable ordinal, and let A(?)κ. If A is an ineffable set, then A is a stationary set and A is the union of κ disjoint stationary sets. We ask the following question: Is A the union of κ disjoint ineffable sets? We will give a positive answer for the question.展开更多
Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable ...Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable as we point out in this paper. In the paper, we give a general definition of fuzzy cardinal numbers. Based on this definition, we not only obtain a large part of results with re spect to cardinal numbers, but also give a few of new properties of fuzzy cardinal numbers.展开更多
The paper introduces the cardinal vowels system invented by the famous English phonetician Daniel Jones.This system enables a teacher to describe to his students a foreign vowel by comparing it with the nearest vowel ...The paper introduces the cardinal vowels system invented by the famous English phonetician Daniel Jones.This system enables a teacher to describe to his students a foreign vowel by comparing it with the nearest vowel in his mother tongue,which makes the learning of a foreign sound much easier to his students.Two cases of teaching Chinese students English vowels are taken as an example to illustrate the point.IPA cardinal vowel system is of use in terms of teaching and learning English.Two suggestions are put forward in the end.展开更多
文摘SOLOVARY proved that every regular uncountable κ is the union of κ disjoint stationary sets (ref. [1], Theorem 85). Let κ be an ineffable ordinal, and let A(?)κ. If A is an ineffable set, then A is a stationary set and A is the union of κ disjoint stationary sets. We ask the following question: Is A the union of κ disjoint ineffable sets? We will give a positive answer for the question.
文摘Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable as we point out in this paper. In the paper, we give a general definition of fuzzy cardinal numbers. Based on this definition, we not only obtain a large part of results with re spect to cardinal numbers, but also give a few of new properties of fuzzy cardinal numbers.
文摘The paper introduces the cardinal vowels system invented by the famous English phonetician Daniel Jones.This system enables a teacher to describe to his students a foreign vowel by comparing it with the nearest vowel in his mother tongue,which makes the learning of a foreign sound much easier to his students.Two cases of teaching Chinese students English vowels are taken as an example to illustrate the point.IPA cardinal vowel system is of use in terms of teaching and learning English.Two suggestions are put forward in the end.
