- arithmetic sentence
- n.算术句子
English-Chinese dictionary of mining (英汉矿业大词典). 2013.
arithmetic sentence
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Non-standard model of arithmetic — In mathematical logic, a nonstandard model of arithmetic is a model of (first order) Peano arithmetic that contains nonstandard numbers. The standard model of arithmetic consists of the set of standard natural numbers {0, 1, 2, …}. The elements… … Wikipedia
Greek arithmetic, geometry and harmonics: Thales to Plato — Ian Mueller INTRODUCTION: PROCLUS’ HISTORY OF GEOMETRY In a famous passage in Book VII of the Republic starting at Socrates proposes to inquire about the studies (mathēmata) needed to train the young people who will become leaders of the ideal… … History of philosophy
Second-order arithmetic — In mathematical logic, second order arithmetic is a collection of axiomatic systems that formalize the natural numbers and sets thereof. It is an alternative to axiomatic set theory as a foundation for much, but not all, of mathematics. The… … Wikipedia
The Foundations of Arithmetic — Die Grundlagen der Arithmetik (The Foundations of Arithmetic) is a book by Gottlob Frege, published in 1884, in which he investigates the philosophical foundations of arithmetic. In a tour de force of literary and philosophical merit, Frege… … Wikipedia
Number sentence — In mathematics education, a number sentence is typically an equation or inequality expressed using numbers and common symbols. The term is used in primary level mathematics teaching in the US[1], Canada, UK[2], Australia, New Zealand[3] and South … Wikipedia
metalogic — /met euh loj ik/, n. the logical analysis of the fundamental concepts of logic. [1835 45; META + LOGIC] * * * Study of the syntax and the semantics of formal languages and formal systems. It is related to, but does not include, the formal… … Universalium
Self-verifying theories — are consistent first order systems of arithmetic much weaker than Peano arithmetic that are capable of proving their own consistency. Dan Willard was the first to investigate their properties, and he has described a family of such systems.… … Wikipedia
Gödel's incompleteness theorems — In mathematical logic, Gödel s incompleteness theorems, proved by Kurt Gödel in 1931, are two theorems stating inherent limitations of all but the most trivial formal systems for arithmetic of mathematical interest. The theorems are of… … Wikipedia
First-order logic — is a formal logical system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic (a less… … Wikipedia
set theory — the branch of mathematics that deals with relations between sets. [1940 45] * * * Branch of mathematics that deals with the properties of sets. It is most valuable as applied to other areas of mathematics, which borrow from and adapt its… … Universalium
Consistency — For other uses, see Consistency (disambiguation). In logic, a consistent theory is one that does not contain a contradiction.[1] The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a … Wikipedia
