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2. Fraction - Wikipedia

   en.wikipedia.org/wiki/Fraction

   The reciprocal of a proper fraction is improper, and the reciprocal of an improper fraction not equal to 1 (that is, numerator and denominator are not equal) is a proper fraction. When the numerator and denominator of a fraction are equal (for example, ⁠ 7 / 7 ⁠), its value is 1, and the fraction therefore is improper. Its reciprocal is ...

3. Partial fraction decomposition - Wikipedia

   en.wikipedia.org/wiki/Partial_fraction_decomposition

   In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator. [1]

4. Solving quadratic equations with continued fractions - Wikipedia

   en.wikipedia.org/wiki/Solving_quadratic...

   By applying the fundamental recurrence formulas we may easily compute the successive convergents of this continued fraction to be 1, 3/2, 7/5, 17/12, 41/29, 99/70, 239/169, ..., where each successive convergent is formed by taking the numerator plus the denominator of the preceding term as the denominator in the next term, then adding in the ...

5. Failure mode and effects analysis - Wikipedia

   en.wikipedia.org/wiki/Failure_mode_and_effects...

   For each component, the failure modes and their resulting effects on the rest of the system are recorded in a specific FMEA worksheet. There are numerous variations of such worksheets. A FMEA can be a qualitative analysis, [ 1 ] but may be put on a quantitative basis when mathematical failure rate models [ 2 ] are combined with a statistical ...

6. List of fallacies - Wikipedia

   en.wikipedia.org/wiki/List_of_fallacies

   2.1 Improper premise. 2.2 Faulty generalizations. ... Archived from the original on 5 July 2014; Sinnott-Armstrong, Walter; Fogelin, Robert (2010). ...

7. Continuous function - Wikipedia

   en.wikipedia.org/wiki/Continuous_function

   For example, if a child grows from 1 m to 1.5 m between the ages of two and six years, then, at some time between two and six years of age, the child's height must have been 1.25 m. As a consequence, if f is continuous on [ a , b ] {\displaystyle [a,b]} and f ( a ) {\displaystyle f(a)} and f ( b ) {\displaystyle f(b)} differ in sign , then, at ...