算术系统

所以更确切地，哥德尔表明，一个形式算术系统，要么不完备，要么不相容。

So more precisely , Gdel had shown that formalised arithmetic must either be inconsistent , or incomplete .

哥德尔继续展示，如何把证明编码，以便整个算术系统都能用算术的方式描述。

Gdel continued to show how to encode proofs as integers , so that he had a whole theory of arithmetic , encoded within arithmetic .

艾伦的问题是，能否把算术系统中所有的不完备性集中起来，集中到一个不能解决的问题上，这个问题就是判定哪些公式是序数公式。

What he asked was whether all the incompleteness of arithmetic could be concentrated in one place , namely into the unsolvable problem of deciding which formulae were ' ordinal formulae ' .

提出了适合于I2L电路及电流型CMOS电路的设计方法，并根据阈算术代数系统及和图方法设计二值、多值I2L电路及电流型CMOS电路。

At last , the binary and multivalued design method of I2L circuits and current-mode CMOS circuits based on threshold-arithmetic algebraic system and HE map is proposed .

本文提出的基于阈算术代数系统及和图的设计方法，使电流型电路的设计变得简单、规范和高效。

The threshold-arithmetic algebraic system is a new simple and effective method for designing the current-mode circuits .

康托用序数来描述他的这些整数序列，而艾伦则把扩展算术公理系统称为序数逻辑。

Cantor had described his different orderings of the integers by ' ordinal numbers ' , and Alan described his different extensions of the axioms of arithmetic as ' ordinal logics ' .

逻辑推理与算术运算合并系统的理论分析

A Theoretical Analysis of Combining System from Logical Reasoning to Arithmetic

根据《九章算术》副词系统的特点把副词分为范围副词、时间副词、程度副词、否定副词、关联副词和情状副词六个部分。

According to Nine Chapters Adverbs characteristics of the system into the scope of the adverb adverbs , time adverbs , degree adverbs , negative adverbs , adverbs and conditions associated with adverbs like six parts .

提出一个逻辑推理与算术运算合并系统的形式定义，通过合并算子把逻辑推理合并到算术系统中，使得在需要解决逻辑推理中的数值计算时，直接把问题转化为纯算术系统中的运算；

A formal system , which combines logical reasoning languages to arithmetic languages through Combining operators , is proposed , so it can be used to solve numeric calculating problems in logical reasoning within pure arithmetic computing systems .

基于模糊数算术运算的信息系统安全性定量评估技术研究

Research on the Technology of Quantitative Security Evaluation Based on Fuzzy Number Arithmetic Operations

总之，他的论点可以应用到任何涵盖了算术公理的形式系统，与其公理本身的内容无关。

However , his argument would apply to any formal mathematical system rich enough to include the theory of numbers , and the details of the axioms were not crucial .

在中国古代，东汉时期的《九章算术》中有系统的分数运算方法，这比欧洲大约早1400年。

Systematic fractional number algorithm appeared in the ancient math classic Jiuzhang Suanshu ( Nine Chapters on Mathematical Art ) in the Eastern Han Dynasty around the 1 st century ， which was about 1400 years ear-tier than in Europe .

验证“模算术”（一种整数的算术系统）的基本性质和解整数系统性质释它在计算机科学中的应用，如在密码学和散列算法。

Prove elementary properties of modular arithmetic and explain their applications in Computer Science , for example , in cryptography and hashing algorithms .