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)
“There is no room for the impurities of literature in an essay.... the essay must be pure—pure like water or pure like wine, but pure from dullness, deadness, and deposits of extraneous matter.”
—Virginia Woolf (1882–1941)
“What’s missing is the eyeballs
in each of us, but it doesn’t matter
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—Anne Sexton (1928–1974)
“The anorexic prefigures this culture in rather a poetic fashion by trying to keep it at bay. He refuses lack. He says: I lack nothing, therefore I shall not eat. With the overweight person, it is the opposite: he refuses fullness, repletion. He says, I lack everything, so I will eat anything at all. The anorexic staves off lack by emptiness, the overweight person staves off fullness by excess. Both are homeopathic final solutions, solutions by extermination.”
—Jean Baudrillard (b. 1929)