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Naive set theory is any of several theories of sets used in the discussion of the foundations of mathematics. Unlike axiomatic set theories, which are defined using formal logic, naive set theory is defined informally, in natural language. It describes the aspects of mathematical sets familiar in discrete mathematics, and suffices for the everyday use of set theory concepts in contemporary mathematics.
In logic, mathematics and linguistics, and is the truth-functional operator of conjunction or logical conjunction. The logical connective of this operator is typically represented as or or (prefix) or or in which is the most modern and widely used.
The Principia Mathematica is a three-volume work on the foundations of mathematics written by mathematician–philosophers Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913. In 1925–1927, it appeared in a second edition with an important Introduction to the Second Edition, an Appendix A that replaced ✱9 and all-new Appendix B and Appendix C. PM was conceived as a sequel to Russell's 1903 The Principles of Mathematics, but as PM states, this became an unworkable suggestion for practical and philosophical reasons: "The present work was originally intended by us to be comprised in a second volume of Principles of Mathematics... But as we advanced, it became increasingly evident that the subject is a very much larger one than we had supposed; moreover on many fundamental questions which had been left obscure and doubtful in the former work, we have now arrived at what we believe to be satisfactory solutions."
In set theory, the union of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations through which sets can be combined and related to each other. A nullary union refers to a union of zero sets and it is by definition equal to the empty set.
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for expressing all mathematics.
In mathematics and computer programming, the order of operations is a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given mathematical expression.
The plus sign and the minus sign are mathematical symbols used to denote positive and negative functions, respectively. In addition, + represents the operation of addition, which results in a sum, while − represents subtraction, resulting in a difference. Their use has been extended to many other meanings, more or less analogous. Plus and minus are Latin terms meaning "more" and "less", respectively.
The multiplication sign, also known as the times sign or the dimension sign, is a mathematical symbol used to denote the operation of multiplication, which results in a product. While similar to a lowercase X, the form is properly a four-fold rotationally symmetric saltire.
Mathematical notation consists of using symbols for representing operations, unspecified numbers, relations, and any other mathematical objects and assembling them into expressions and formulas. Mathematical notation is widely used in mathematics, science, and engineering for representing complex concepts and properties in a concise, unambiguous, and accurate way.
In mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence of symbols from a given alphabet that is part of a formal language. A formal language can be identified with the set of formulas in the language.
The Attic numerals are a symbolic number notation used by the ancient Greeks. They were also known as Herodianic numerals because they were first described in a 2nd-century manuscript by Herodian; or as acrophonic numerals because the basic symbols derive from the first letters of the (ancient) Greek words that the symbols represented.
The infinity symbol is a mathematical symbol representing the concept of infinity. This symbol is also called a lemniscate, after the lemniscate curves of a similar shape studied in algebraic geometry, or "lazy eight", in the terminology of livestock branding.
Mathematical software is software used to model, analyze or calculate numeric, symbolic or geometric data.
Arithmetica is an Ancient Greek text on mathematics written by the mathematician Diophantus in the 3rd century AD. It is a collection of 130 algebraic problems giving numerical solutions of determinate equations and indeterminate equations.
Pierre Hérigone (1580–1643) was a French mathematician and astronomer.
An arrow is a graphical symbol, such as ← or →, or a pictogram, used to point or indicate direction. In its simplest form, an arrow is a triangle, chevron, or concave kite, usually affixed to a line segment or rectangle, and in more complex forms a representation of an actual arrow. The direction indicated by an arrow is the one along the length of the line or rectangle toward the single pointed end.
The history of mathematical notation includes the commencement, progress, and cultural diffusion of mathematical symbols and the conflict of the methods of notation confronted in a notation's move to popularity or inconspicuousness. Mathematical notation comprises the symbols used to write mathematical equations and formulas. Notation generally implies a set of well-defined representations of quantities and symbols operators. The history includes Hindu–Arabic numerals, letters from the Roman, Greek, Hebrew, and German alphabets, and a host of symbols invented by mathematicians over the past several centuries.
Mathematics is a field of study that investigates topics such as number, space, structure, and change.
In computer science, a symbolic language is a language that uses characters or symbols to represent concepts, such as mathematical operations and the entities on which these operations are performed.
In engineering, a symbolic language is a language that uses standard symbols, marks, and abbreviations to represent concepts such as entities, aspects, attributes, and relationships.
References
- ↑ "symbolic language Definition from PC Magazine Encyclopedia". www.pcmag.com. Retrieved 2019-03-23.
- ↑ "A Handbook of Mathematical Discourse". 2009. CiteSeerX 10.1.1.217.5892 .
