Table of Contents

## What is the name of theorem 1?

Theorem 1: Equal chords of a circle subtend equal angles, at the centre of the circle. Converse of Theorem 1: If two angles subtended at the centre, by two chords are equal, then the chords are of equal length.

**What is the most famous theorem?**

The Pythagorean Theorem is arguably the most famous statement in mathematics, and the fourth most beautiful equation.

### What is meant by Thales theorem?

In geometry, Thales’ theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ABC is a right angle. Thales’s theorem is a special case of the inscribed angle theorem and is mentioned and proved as part of the 31st proposition in the third book of Euclid’s Elements.

**Does the Cantor–Schroeder–Bernstein theorem hold in a Boolean topos?**

However, the theorem actually requires only excluded middle, although it does not hold in constructive mathematics — indeed, it is actually equivalent to excluded middle (at least assuming the axiom of infinity ). We prove that the Cantor–Schroeder–Bernstein theorem holds in a Boolean topos.

#### What is the Schröder–Bernstein theorem?

In set theory, the Schröder–Bernstein theorem states that, if there exist injective functions f : A → B and g : B → A between the sets A and B, then there exists a bijective function h : A → B.

**What is the Cantor-Schröder-Bernstein theorem?**

This is called the Cantor-Schröder-Bernstein Theorem. See Wikipedia for another writeup. First a reminder of some relevant definitions: A function f: A → B is one-to-one if for all x 1 and x 2 ∈ A, f ( x 1) ≠ f ( x 2) unless x 1 = x 2.

## Does EM constructively follow from the Cantor-Schroeder-Bernstein statement?

In fact EM does constructively follow from the Cantor-Schroeder-Bernstein statement provided that a natural numbers object exists; see Pradic and Brown, 2019. A proof that in a topos CSB+NNO implies Booleanness is outlined in Freyd 1994.