### Some articles on *upper bound principle, upper bound, principle*:

Constructive Analysis - Examples - The Least

... is that constructive analysis does not accept the least

**Upper Bound Principle**and Compact Sets... is that constructive analysis does not accept the least

**upper bound principle**, that any subset of the real line R has a least**upper bound**(or supremum ... exists an element s of S such that x < s, or y is an**upper bound**of S.) Again, this is classically equivalent to the full least**upper bound principle**, since every set is located in ...Specker Sequence

... exist means that the collection of all computable real numbers does not satisfy the least

... exist means that the collection of all computable real numbers does not satisfy the least

**upper bound principle**of real analysis, even when considering only computable sequences ... The least**upper bound principle**has also been analyzed in the program of reverse mathematics, where the exact strength of this**principle**has been determined ... In the terminology of that program, the least**upper bound principle**is equivalent to ACA0 over RCA0 ...### Famous quotes containing the words principle, upper and/or bound:

“Now, what I want is, Facts. Teach these boys and girls nothing but Facts. Facts alone are wanted in life. Plant nothing else, and root out everything else. You can only form the minds of reasoning animals upon Facts: nothing else will ever be of any service to them. This is the *principle* on which I bring up my own children, and this is the *principle* on which I bring up these children. Stick to Facts, sir!”

—Charles Dickens (1812–1870)

“Surely you wouldn’t grudge the poor old man

Some humble way to save his self-respect.

He added, if you really care to know,

He meant to clear the *upper* pasture, too.”

—Robert Frost (1874–1963)

“In the word of no master am I *bound* to believe.”

—Horace [Quintus Horatius Flaccus] (65–8 B.C.)

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