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The function f is continuous at p if and only if the limit of f(x) as x approaches p exists and is equal to f(p). If f : M → N is a function between metric spaces M and N, then it is equivalent that f transforms every sequence in M which converges towards p into a sequence in N which converges towards f(p).
In the present day, the distinction between pure and applied mathematics is more a question of personal research aim of mathematicians than a division of mathematics into broad areas. [ 124 ] [ 125 ] The Mathematics Subject Classification has a section for "general applied mathematics" but does not mention "pure mathematics". [ 14 ]
Flowering plants are plants that bear flowers and fruits, and form the clade Angiospermae (/ ˌ æ n dʒ i ə ˈ s p ər m iː /). [5] [6] The term 'angiosperm' is derived from the Greek words ἀγγεῖον / angeion ('container, vessel') and σπέρμα / sperma ('seed'), meaning that the seeds are enclosed within a fruit.
The energy needed to build a wind farm divided into the total output over its life, Energy Return on Energy Invested, of wind power varies, but averages about 20–25. [ 85 ] [ 86 ] Thus, the energy payback time is typically around a year.
Spanish explorers were the first Europeans, after the Norse, to reach the present-day United States, after the voyages of Christopher Columbus (beginning in 1492) established possessions in the Caribbean, including the modern-day U.S. territories of Puerto Rico, and parts of the U.S. Virgin Islands. Juan Ponce de León landed in Florida in 1513 ...
The diversity of life on Earth is a result of the dynamic interplay between genetic opportunity, metabolic capability, environmental challenges, [95] and symbiosis. [96] [97] [98] For most of its existence, Earth's habitable environment has been dominated by microorganisms and subjected to their metabolism