Print Advertisement John T. Russell's paradox is based on examples like this: Consider a group of barbers who shave only those men who do not shave themselves.
MaxW Thank you for your time and for your answer. Bertrand paradox my perspective, I find your confirmation about the question not being an actual paradox really important. Bertrand paradox in your answer extends beyond "Wikipedia" and gives directions for further research.
As for the process of choosing a random variable, I see it as a "reference axis" for probability distribution and might post a question regarding this topic after more research.
That is to say does it have an unique solution. IMHO the following holds: This reasoning is valid: For every Radius there is only one chord which bisets it a right angles, it has the length of the side of the triangle.
There exists an infinite number of chords on the "inside half" towards the center as well on the "outside half" towards the circumferencethe outer half being shorter, the inner half being longer then the side.
As any radius including its associated chords can be obtained from any other by simple rotation, the ratio of longer to shorter chords is 1: When analysing selection method one as given by Bertrand, one finds that this selection method generates a subset of all existing chords only chords on radii pointing to the arc running from through 0 to 90 degreesand only the chords bisected at right angles by the radii conncting to the arcs between 60 and 90, and and respectively, are longer then the side.
Considering method three remember that all chords are bisected at right angles by a radius, and every radius bisects in this way an infinite number of chords.
Furthermore, the circles are concentric the have the same midpoint. It also holds that a radius runs from the centre of the circle to a point on the circumference.
As a consequence, all radii of the outer circle pass throug the inner circle, and their "inner halfs" are a radius of the inner circle. The argument that a bigger arae implies more chords is clearly false, if correct it would imply that there are more radii existing in the ring, which is not possible as every radius has to connect to the center, and every additional radius would increase the number of radii in the inner circle, and consequently the number of chords.
Further reading on this problem quickly exceeded my mathematics, and it will take some time to understand the beginning of the complications that according to the professionals do exist, if ever.Russell’s paradox is the most famous of the logical or set-theoretical paradoxes.
Also known as the Russell-Zermelo paradox, the paradox arises within naïve set theory by considering the set of all sets that are not members of themselves. What is the Bertrand's paradox? It is the following problem: Find the probability that the length of a random chord will be greater than the side of an equilateral triangle inscribed in that circle.
First example: A chord is fully determined by its midpoint. Chords whose length exceeds the side of an equilateral triangle have their midpoints closer to the center than half the radius, the probability becomes 1/2.
Meng-YuLiang NTUIO(I):Bertrand Paradox 2 Bertrand Paradox. Inrealworldusuallyweusepriceasstrategyratherthanquantity. WelikeCournot’sresult, butwedon’tlikeitsapproach. Bertrand Russell's discovery of this paradox in dealt a blow to one of his fellow mathematicians.
In the late s, Gottlob Frege tried to develop a foundation for all of mathematics using symbolic logic. A paradox connected with an inaccurate formulation of the initial assumptions in solving problems in probability.
Noted by J. Bertrand. Bertrand's problem is concerned with the probability that the length of a chord, chosen at random in a disc of radius one, is larger than the side length of the inscribed equilateral triangle. The Bertrand paradox is a problem within the classical interpretation of probability theory.
Joseph Bertrand introduced it in his work Calcul des probabilités () as an example to show that probabilities may not be well defined if the mechanism or method that produces the .
Bertrand's Paradox. Theory of Probability (much as the rest of Mathematics) is actually a recent invention. And the development has not been smooth at all. A great analysis of this paradox, known as Edgeworth duopoly model or Bertrand-Edgeworth duopoly, was developed by Francis Y. Edgeworth in his paper “The Pure Theory of Monopoly”, A great analysis of this paradox, known as Edgeworth duopoly model or Bertrand-Edgeworth duopoly, was developed by Francis Y. Edgeworth in his paper “The Pure Theory of Monopoly”, What is the Bertrand's paradox? It is the following problem: Find the probability that the length of a random chord will be greater than the side of an equilateral triangle inscribed in that circle. First example: A chord is fully determined by its midpoint. Chords whose length exceeds the side of an equilateral triangle have their midpoints closer to the center than half the radius, the probability becomes 1/2.