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The notion of irreducible fraction generalizes to the field of fractions of any unique factorization domain: any element of such a field can be written as a fraction in which denominator and numerator are coprime, by dividing both by their greatest common divisor. [7] This applies notably to rational expressions over a field. The irreducible ...
Another kind of fraction is the percentage (from Latin: per centum, meaning "per hundred", represented by the symbol %), in which the implied denominator is always 100. Thus, 51% means 51/100. Percentages greater than 100 or less than zero are treated in the same way, e.g. 311% equals 311/100, and −27% equals −27/100.
Simplification is the process of replacing a mathematical expression by an equivalent one that is simpler (usually shorter), according to a well-founded ordering. Examples include:
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An overline, overscore, or overbar, is a typographical feature of a horizontal line drawn immediately above the text. In old mathematical notation, an overline was called a vinculum, a notation for grouping symbols which is expressed in modern notation by parentheses, though it persists for symbols under a radical sign.
Utilizing one of these isomorphisms can simplify the mathematical considerations as the degree of the extension is smaller with the trade off that the elements are now represented over a larger subfield. [9] To reduce gate count for hardware implementations, the process may involve multiple nesting, such as mapping from GF(2 8) to GF(((2 2) 2 ...
In his article, Miller discussed a coincidence between the limits of one-dimensional absolute judgment and the limits of short-term memory. In a one-dimensional absolute-judgment task, a person is presented with a number of stimuli that vary on one dimension (e.g., 10 different tones varying only in pitch) and responds to each stimulus with a corresponding response (learned before).
It is also a sphenic number, [3] an extravagant number, [4] a lucky number, [5] a polite number, [6] an amenable number, and a deficient number. 777 is a congruent number, [7] as it is possible to make a right triangle with a rational number of sides whose area is 777. [8]