Analytic Proof
In mathematical analysis, an analytical proof is a proof of a theorem in analysis that only makes use of methods from analysis, and which does not make use of results from geometry. The term was first used by Bernard Bolzano, who first provided a non-analytic proof of his intermediate value theorem and then, several years later provided proof of the theorem which was free from intuitions concerning lines crossing each other at a point and so he felt happy calling analytic (Bolzano 1817).
Bolzano's philosophical work encouraged a more abstract reading of when a demonstration could be regarded as analytic, where a proof is analytic if it does not go beyond its subject matter (Sebastik 2007). In proof theory, an analytical proof has come to mean a proof whose structure is simple in a special way, due to conditions on the kind of inferences that ensure none of them go beyond what is contained in the assumptions and what is demonstrated.
Read more about Analytic Proof: Structural Proof Theory
Famous quotes containing the words analytic and/or proof:
““You, that have not lived in thought but deed,
Can have the purity of a natural force,
But I, whose virtues are the definitions
Of the analytic mind, can neither close
The eye of the mind nor keep my tongue from speech.””
—William Butler Yeats (1865–1939)
“If we view our children as stupid, naughty, disturbed, or guilty of their misdeeds, they will learn to behold themselves as foolish, faulty, or shameful specimens of humanity. They will regard us as judges from whom they wish to hide, and they will interpret everything we say as further proof of their unworthiness. If we view them as innocent, or at least merely ignorant, they will gain understanding from their experiences, and they will continue to regard us as wise partners.”
—Polly Berrien Berends (20th century)