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The absolute value of a number may be thought of as its distance from zero. In mathematics, the absolute value or modulus of a real number , denoted , is the non-negative value of without regard to its sign. Namely, if is a positive number, and if is negative (in which case negating makes positive), and . For example, the absolute value of 3 is ...
Mathematical beauty is the aesthetic pleasure derived from the abstractness, purity, simplicity, depth or orderliness of mathematics. Mathematicians may express this pleasure by describing mathematics (or, at least, some aspect of mathematics) as beautiful or describe mathematics as an art form, (a position taken by G. H. Hardy [ 1]) or, at a ...
The mathematician Jerry P. King describes mathematics as an art, stating that "the keys to mathematics are beauty and elegance and not dullness and technicality", and that beauty is the motivating force for mathematical research. [91] King cites the mathematician G. H. Hardy's 1940 essay A Mathematician's Apology.
The face value, sometimes called nominal value, is the value of a coin, bond, stamp or paper money as printed on the coin, stamp or bill itself [1] by the issuing authority. The face value of coins, stamps, or bill is usually its legal value. However, their market value need not bear any relationship to the face value.
Glossary of mathematical symbols. 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 ...
Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures ...
projection. A projection is, roughly, a map from some space or object to another that omits some information on the object or space. For example, R 2 → R , ( x , y ) ↦ x {\displaystyle \mathbb {R} ^ {2}\to \mathbb {R} , (x,y)\mapsto x} is a projection and its restriction to a graph of a function, say, is also a projection.
A Mathematician's Apology is a 1940 essay by British mathematician G. H. Hardy, which offers a defence of the pursuit of mathematics. Central to Hardy's "apology" – in the sense of a formal justification or defence (as in Plato 's Apology of Socrates) – is an argument that mathematics has value independent of possible applications. Hardy ...