A Note on Transfinite Cardinal Numbers
- A Note on Transfinite Cardinal Numbers
- Other Titles
- 超限基數들에 關한 考察
- Park, Yong Sik
- Issue Date
- No. 2
- 本 論文은 超限基數들(또는 無限集合의 基數들)에 關한 것이다. 論文의 目的은 有限集合의 基數들의 性質을 알고 超限基數들(Χ_0, C, 2^Χ_0, 2^C, Χ_0^Χ_0, Χ_0^C, C_Χ_0, C^C)의 一般的 特性을 조사하여 그들간의 相互關係를 硏究하는데 있다.
This paper is concerned with transfinite cardinal numbers(or the cardinal number of infinite sets). The purpose is to investigate the general properties of transfinite cardinal numbers(Χ_0, C, 2^Χ_0, 2^C, Χ_0^Χ_0, Χ_0^C, C_Χ_0, C^C) and study their correlations as follows: 1. Algebraic numbers and Χ_0. 2. Other sets with cardinality c and Χ_0. 3. Cardinal exponents and Χ_0, C. 4. The cardinality of the set of function and subset. Cardinalities are to be well-defined sets, and every set is to be equipotent with exactly one cardinal number. The cardinal number of any denumerable set is customarily designated by the symbolΧ.(aleph-null). It is useftl to distinguish between finite cardinal numbers-that is, cardinal numbers of finite sets-and infinite, or transfinite cardinal numbers, which are the cardinal number of infinite sets. We shall show to investigate a general definition of cardinal numbers of infinite sets, or transfinite cardinal numbers.
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