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An example of "beauty in method"—a simple and elegant visual descriptor of the Pythagorean theorem. 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 ...
Validity (statistics) Validity is the main extent to which a concept, conclusion, or measurement is well-founded and likely corresponds accurately to the real world. [ 1][ 2] The word "valid" is derived from the Latin validus, meaning strong. The validity of a measurement tool (for example, a test in education) is the degree to which the tool ...
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.
Some of Hilbert's statements were not precise enough to specify a particular problem, but were suggestive enough that certain problems of contemporary nature seem to apply; for example, most modern number theorists would probably see the 9th problem as referring to the conjectural Langlands correspondence on representations of the absolute ...
On eBay, these kinds of bills can sell for anywhere from $10 to $300. The lower the serial number, the more valuable the currency is considered to be; a bill with the serial number 00000001 could ...
Valuation (algebra) In algebra (in particular in algebraic geometry or algebraic number theory ), a valuation is a function on a field that provides a measure of the size or multiplicity of elements of the field. It generalizes to commutative algebra the notion of size inherent in consideration of the degree of a pole or multiplicity of a zero ...
Intermediate value theorem: Let be a continuous function defined on [,] and let be a number with () < < ().Then there exists some between and such that () =.. In mathematical analysis, the intermediate value theorem states that if is a continuous function whose domain contains the interval [a, b], then it takes on any given value between () and () at some point within the interval.
The fact–value distinction is also closely related to the moralistic fallacy, an invalid inference of factual conclusions from purely evaluative premises. For example, an invalid inference "Because everybody ought to be equal, there are no innate genetic differences between people" is an instance of the moralistic fallacy.