无限集合

[推论1]至少有1个3生素数集合（或称3素数组子集）是无限集合；

[ Corollary 1 ] There exists at least one of the sets of primes-triplet ( namely one subset of the set of 3-primes-group ), which is an infinite set .

所谓多重分形，是定义在分形结构上的由多个标度指数的分形测度组成的无限集合，它刻画了分布在子集上的具有不同标度和标度指数的分形子集的局部标度性。

The so-called multifractal , which is defined on a fractal structure , is an infinite set composed by fractal measure of many scaling exponents . It depicts the local scale of fractal subset with different scales and scaling exponents .

当论域I为有限集合，J为无限集合时，给出了存在可达解以及存在极小解的充要条件。

When the domain / is finite , J is infinite , sufficient and necessary conditions for existences of an attainable solution and a minimal solution are obtained .

无限集合的有限子集理论的等价转化

Elementary Conversion of the Theory for all the Finite Subset of Finite Set

比如说，我可能知道康托尔的理论，无限集合也有大小之分，

I might know , you know , Cantor 's idea that some infinite sets are larger than other infinite sets ,

本文通过重新定义模糊集合的包含度和相交度概念，将模糊证据理论推广到识别框架为连续无限集合的情形，并将其成功应用于产品的可靠性评估工作之中。

The concepts of inclusion degree and intersection degree of fuzzy sets were redefined , and fuzzy evidence theory was extended to the circumstance when the framework of discrimination is a continuous and infinite set . The generalized fuzzy evidence theory was applied to reliability assessment successfully .

并提出了一种自动验证参数化LE协议的方法，用线性算数约束来模拟可能无限的全局状态集合，利用符号模型检测工具DMC[DP99]，文章实现了对参数化LE协议safety性质的自动验证。

This approach uses linear arithmetic constraints to model possibly infinite sets of global states . Using symbolic model checker DMC [ DP99 ] , it automatically verifies safety properties for parameterized Leader Election protocols .

无穷观问题的研究（Ⅴ）&一个兼容实无限与潜无限的公理集合论系统APAS

An Outlook on the Infinity (ⅴ) - An Axiomatic Set Theory APAS for Holding the Actual Infinity and the Potential Infinity Concurrently

[推论2]全部的或无限多的3生素数集合是无限集合；

[ Corollary 2 ] All the sets of primes-triplet or infinitely many ones among these sets are infinite sets .