Extraneous And Missing Solutions
In mathematics, an extraneous solution represents a solution, such as that to an equation, that emerges from the process of solving the problem but is not a valid solution to the original problem. A missing solution is a solution that was a valid solution to the original problem, but disappeared during the process of solving the problem. Both are frequently the consequence of performing operations that are not invertible for some or all values of the variables, which disturbs the chain of logical implications in the proof.
Read more about Extraneous And Missing Solutions: Extraneous Solutions: Multiplication, Extraneous Solutions: Rational, Missing Solutions: Division, Other Operations
Famous quotes containing the words extraneous and, extraneous, missing and/or solutions:
“If intellection and knowledge were mere passion from without, or the bare reception of extraneous and adventitious forms, then no reason could be given at all why a mirror or looking-glass should not understand; whereas it cannot so much as sensibly perceive those images which it receives and reflects to us.”
—Ralph J. Cudworth (1617–1688)
“If intellection and knowledge were mere passion from without, or the bare reception of extraneous and adventitious forms, then no reason could be given at all why a mirror or looking-glass should not understand; whereas it cannot so much as sensibly perceive those images which it receives and reflects to us.”
—Ralph J. Cudworth (1617–1688)
“I am opposed to writing about the private lives of living authors and psychoanalyzing them while they are alive. Criticism is getting all mixed up with a combination of the Junior F.B.I.- men, discards from Freud and Jung and a sort of Columnist peep- hole and missing laundry list school.... Every young English professor sees gold in them dirty sheets now. Imagine what they can do with the soiled sheets of four legal beds by the same writer and you can see why their tongues are slavering.”
—Ernest Hemingway (1899–1961)
“Science fiction writers foresee the inevitable, and although problems and catastrophes may be inevitable, solutions are not.”
—Isaac Asimov (1920–1992)