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The word proof derives from the Latin probare 'to test'; related words include English probe, probation, and probability, as well as Spanish probar 'to taste' (sometimes 'to touch' or 'to test'), [5] Italian provare 'to try', and German probieren 'to try'.
In mathematics, an extraneous solution (or spurious solution) is one which emerges from the process of solving a problem but is not a valid solution to it. [1] A missing solution is a valid one which is lost during the solution process.
Dimensional analysis may be used as a sanity check of physical equations: the two sides of any equation must be commensurable or have the same dimensions. A person who has calculated the power output of a car to be 700 kJ may have omitted a factor, since the unit joules is a measure of energy, not power (energy per unit time).
The seemingly "simple" elementary brain-teaser asks one student "Reasonableness: Marty ate 4/6 of his pizza and Luis ate 5/6 of his pizza. Marty ate more pizza than Luis.
The system + =, + = has exactly one solution: x = 1, y = 2 The nonlinear system + =, + = has the two solutions (x, y) = (1, 0) and (x, y) = (0, 1), while + + =, + + =, + + = has an infinite number of solutions because the third equation is the first equation plus twice the second one and hence contains no independent information; thus any value of z can be chosen and values of x and y can be ...
Another notable case were "Fermatists", who plagued mathematical institutions with requests to check their proofs of Fermat's Last Theorem. [ 7 ] [ 8 ] Another common approach is to misapprehend standard mathematical methods, and to insist that the use or knowledge of higher mathematics is somehow cheating or misleading (e.g., the denial of ...
Roberto Poli of McGill University delivered a number of lectures entitled The unreasonable ineffectiveness of mathematics in cognitive sciences in 1999. The abstract is: My argument is that it is possible to gain better understanding of the "unreasonable effectiveness" of mathematics in study of the physical world only when we have understood the equally "unreasonable ineffectiveness" of ...
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