Concept
Numeral system
Overview
notation for expressing numbers
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
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In mathematics, the formal impulse to reduce the content of fundamental concepts to a minimum, and to stress merely relations has been most successful. We saw its results in such geometries as Hilbert's and Peano's, where the empty name "entity" supplants the more concrete "point," and the "1" of arithmetic has the same character. In the social sciences, however, such examples as the "political" and the "economic"…
John Dewey, Creative Intelligence
Close in meaning to Numeral system; the term itself is not named.
"Let us take as the basis of our consideration first of all a thought-thing 1 (one)" (p. 341). Notice that in so doing we in no wise imply the notion of number, because it is understood that 1 is here only a symbol and that we do not at all seek to know its meaning. "The taking of this thing together with itself respectively two, three or more times...." Ah!
Henri Poincaré, The Foundations of Science
States what Numeral system is.
The system of general language called algebraical notation does this. The expressions _a_ and a2+3a denote, the one any number, the other the number formed from it in a particular manner. The expressions _a_, _b_, _n_, and (_a+b_)n, denote any three numbers, and a fourth which is formed from them in a certain mode. The following may be stated as the general problem of the algebraical calculus: F being a certain…
John Stuart Mill, A System of Logic, Ratiocinative and Inductive
Close in meaning to Numeral system; the term itself is not named.
Related ideas
- Glyph
- Integer
- If and only if
- Japan
- Fibonacci
- Algebra
- Islamic world
- Rational number
- Real number
- Natural number
- Number
- Writing system
- Arithmetic
- Theoretical computer science
- 0
- Bijection
- Egyptian hieroglyphs
- China
- Complex number
- Decimal
- Ancient Egypt
Opposing perspectives
Place in the tradition
Part of Philosophy of mathematics.