In set theory and other branches of mathematics, ב2 (pronounced beth two), or 2c (pronounced two to the power of c), is a certain cardinal number. It is the 2nd beth number, and is the result of cardinal exponentiation when 2 is raised to the power of c, the cardinality of the continuum.
The power set of the power set of the set of natural numbers, so it is the number of sets of sets of natural numbers;
The set of all functions from the real line to itself;
The power set of the set of all functions from the set of natural numbers to itself, so it is the number of sets of sequences of natural numbers;
The set of all real-valued functions of n real variables to the real numbers.
Some early set theorists hypothesised the equation
stating that 2c is equal to the 2nd aleph number. It turns out that the truth of this equation (*) cannot be determined from the standard Zermelo-Fraenkel axioms of set theory; it is true in some models and false in others. (*) is a part of the generalized continuum hypothesis (GCH), but it is possible that (*) is true while the full GCH is false. On the other hand, if (*) is true, then the ordinary continuum hypothesis (CH) must follow, but again it is possible that CH is true while (*) is false.
This article or a past revision is based on the Mandelbrot Set Glossary and Encyclopedia (http://www.mrob.com/pub/muency.html), copyright 1987-2003 Robert P. Munafo, which is made available under the terms of the GNU Free Documentation License.
In the vast majority of the world's nuclear power plants, heat energy generated by fissioning uranium fuel is collected in purified water and is carried away from the reactor's core either as steam in boiling water reactors or as superheated water in pressurized-water reactors.
Some early power stations were fast reactors, as are some Russian naval propulsion units, and construction of prototypes is continuing, see fast breeder, but overall the class has not achieved the success of thermal reactors in any application.
Proponents of nuclear power maintain that nuclear energy is the only power source which explicitly factors the estimated cost of waste containment and plant decommissioning into its overall cost, and that the quoted cost of fossil fuel plants is deceptively low for this reason.
There are two types of solar power: solar thermal power and photovoltaic power.
A solar thermal power plant has a system of mirrors to concentrate the sunlight on to an absorber, the energy then being used to drive turbines or a thermocouple.
Direct electricity generation by solar power has several difficulties; though the sun puts out a vast quantity of energy, that energy is relatively diffuse and intermittent.
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