Abel's Test - Abel's Test in Real Analysis

Famous quotes containing the words test, real and/or analysis:

“[17th-century] Puritans were the first modern parents. Like many of us, they looked on their treatment of children as a test of their own self-control. Their goal was not to simply to ensure the child’s duty to the family, but to help him or her make personal, individual commitments. They were the first authors to state that children must obey God rather than parents, in case of a clear conflict.”
—C. John Sommerville (20th century)

“All ... forms of consensus about “great” books and “perennial” problems, once stabilized, tend to deteriorate eventually into something philistine. The real life of the mind is always at the frontiers of “what is already known.” Those great books don’t only need custodians and transmitters. To stay alive, they also need adversaries. The most interesting ideas are heresies.”
—Susan Sontag (b. 1933)

“Analysis as an instrument of enlightenment and civilization is good, in so far as it shatters absurd convictions, acts as a solvent upon natural prejudices, and undermines authority; good, in other words, in that it sets free, refines, humanizes, makes slaves ripe for freedom. But it is bad, very bad, in so far as it stands in the way of action, cannot shape the vital forces, maims life at its roots. Analysis can be a very unappetizing affair, as much so as death.”
—Thomas Mann (1875–1955)