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theorem$82791$ - translation to greek

THEOREM

Lob's Theorem; Löb's Theorem; Lob's theorem; Loeb's theorem; Loeb theorem; Lob theorem; Löb theorem; Loeb's Theorem

theorem

n. θεώρημα

inscribed angle

$Animated gif of proof of the inscribed angle theorem. The large triangle that is inscribed in the circle gets subdivided into three smaller triangles, all of which are isosceles because their upper two sides are radii of the circle. Inside each isosceles triangle the pair of base angles are equal to each other, and are half of 180° minus the apex angle at the circle's center. Adding up these isosceles base angles yields the theorem, namely that the inscribed angle, <math> \psi </math>, is half the central angle, <math> \theta </math>.$

ANGLE FORMED IN THE INTERIOR OF A CIRCLE

Inscribed angle theorem

εγγεγραμένη γωνία

absolute convergence

A PROPERTY OF INFINITE SERIES

Absolut convergence; Absolutely convergent; Absolute Convergence; Absolutely convergent series; Absolutely convergent improper integral; Absolute summability; Converges absolutely; Unconditional summability; Absolute convergence theorem; Absolutely summable

απόλυτη σύγκριση

Definition

theorem

n.

Proposition (to be demonstrated), position, dictum, thesis.

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Wikipedia

Löb's theorem

In mathematical logic, Löb's theorem states that in Peano arithmetic (PA) (or any formal system including PA), for any formula P, if it is provable in PA that "if P is provable in PA then P is true", then P is provable in PA. If Prov(P) means that the formula P is provable, we may express this more formally as

If

PA\,\vdash \,{{\rm {Prov}}(P)\rightarrow P}

then

PA\,\vdash \,P

An immediate corollary (the contrapositive) of Löb's theorem is that, if P is not provable in PA, then "if P is provable in PA, then P is true" is not provable in PA. For example, "If $1+1=3$ is provable in PA, then $1+1=3$ " is not provable in PA.

Löb's theorem is named for Martin Hugo Löb, who formulated it in 1955. It is related to Curry's paradox.

https://en.wikipedia.org/wiki/Löb's theorem