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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.
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.
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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.
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.
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One way of mapping terrestrial biomes around the world (except the Antarctic Tundra) A biome (/ ˈ b aɪ. oʊ m /) is a distinct geographical region with specific climate, vegetation, and animal life. It consists of a biological community that has formed in response to its physical environment and regional climate. [1]
Alaska is the most biodiverse state with 15 ecoregions across three biomes in the same realm. California comes in a close second with 13 ecoregions across four biomes in the same realm. By contrast, Rhode Island is the least biodiverse with just one ecoregion—the Northeastern coastal forests —encompassing the entire state.