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In mathematics, the term undefined refers to a value, function, or other expression that cannot be assigned a meaning within a specific formal system. [ 1 ] Attempting to assign or use an undefined value within a particular formal system, may produce contradictory or meaningless results within that system.
The necessity for primitive notions is illustrated in several axiomatic foundations in mathematics: Set theory: The concept of the set is an example of a primitive notion. As Mary Tiles writes: [6] [The] 'definition' of 'set' is less a definition than an attempt at explication of something which is being given the status of a primitive ...
Although applicable to any area of mathematics, geometry is the branch of elementary mathematics in which this method has most extensively been successfully applied. [1] There are several components of an axiomatic system. [2] Primitives (undefined terms) are the most basic ideas. Typically they include objects and relationships.
Mathematical notation is widely used in mathematics, science, and engineering for representing complex concepts and properties in a concise, unambiguous, and accurate way. For example, the physicist Albert Einstein 's formula E = m c 2 {\displaystyle E=mc^{2}} is the quantitative representation in mathematical notation of mass–energy ...
This is the same as Euclid's method of treating point and line as undefined primitive notions and axiomatizing their relationships. Great circles in many ways play the same logical role in spherical geometry as lines in Euclidean geometry, e.g., as the sides of (spherical) triangles.
The Mathematical Alphanumeric Symbols block (U+1D400–U+1D7FF) contains Latin and Greek letters and decimal digits that enable mathematicians to denote different notions with different letter styles. The reserved code points (the "holes") in the alphabetic ranges up to U+1D551 duplicate characters in the Letterlike Symbols block. In order ...
Foundations and Fundamental Concepts of Mathematics. Dover. Chpt. 4.2 covers the Hilbert axioms for plane geometry. Ivor Grattan-Guinness, 2000. In Search of Mathematical Roots. Princeton University Press. David Hilbert, 1980 (1899). The Foundations of Geometry, 2nd ed. Chicago: Open Court.
The expression is undefined [1] and must be avoided. A finite signed measure (a.k.a. real measure ) is defined in the same way, except that it is only allowed to take real values. That is, it cannot take + ∞ {\displaystyle +\infty } or − ∞ . {\displaystyle -\infty .}