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The goal is to prove that the axiom of choice is implied by the statement "for every infinite set : | | = | |".It is known that the well-ordering theorem is equivalent to the axiom of choice; thus it is enough to show that the statement implies that for every set there exists a well-order.
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This is a list of fictional settlements, including fictional towns, villages, and cities, organized by each city's medium.This list should include only well-referenced, notable examples of fictional towns, cities, settlements and villages that are integral to a work of fiction and substantively depicted therein.
This is a list of terrestrial ecoregions as compiled by the World Wildlife Fund (WWF). The WWF identifies terrestrial, freshwater, and marine ecoregions. The terrestrial scheme divides the Earth's land surface into 8 biogeographic realms, containing 867 smaller ecoregions. Each ecoregion is classified into one of 14 major habitat types, or biomes.
These axioms are sufficient for many proofs in elementary mathematical analysis, and are consistent with some principles, such as the Lebesgue measurability of all sets of reals, that are disprovable from the full axiom of choice. Given an ordinal parameter α ≥ ω+2 — for every set S with rank less than α, S is well-orderable.
They are distinct from biomes, also known as major habitat types, which are divisions of the Earth's surface based on life form, or the adaptation of animals, fungi, micro-organisms and plants to climatic, soil, and other conditions. Biomes are characterized by similar climax vegetation. Each realm may include a number of different biomes.
A fictional Indian town, which was once a dense forest, a desert, a village, an empire, a junkyard, a market square, a city of Muslims, a British state, and a place where military training was given. Now it is a small town with 1336 residents, among them, 600 are educated. In the future it will be a tech city full of cars.
The village categories for some countries are combined with categories for other types of settlements because no official distinction is made locally. See also: Category:Populated places by country Subcategories