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Rigor is a cornerstone quality of mathematics, and can play an important role in preventing mathematics from degenerating into fallacies. well-behaved An object is well-behaved (in contrast with being Pathological ) if it satisfies certain prevailing regularity properties, or if it conforms to mathematical intuition (even though intuition can ...
2. Equivalence class: given an equivalence relation, [] often denotes the equivalence class of the element x. 3. Integral part: if x is a real number, [] often denotes the integral part or truncation of x, that is, the integer obtained by removing all digits after the decimal mark.
Also called infinitesimal calculus A foundation of calculus, first developed in the 17th century, that makes use of infinitesimal numbers. Calculus of moving surfaces an extension of the theory of tensor calculus to include deforming manifolds. Calculus of variations the field dedicated to maximizing or minimizing functionals. It used to be called functional calculus. Catastrophe theory a ...
German mathematician Carl Friedrich Gauss said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theory also studies the natural, or whole, numbers. One of the central concepts in number theory is that of the prime number , and there are many questions about primes that appear simple but whose ...
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Mathematics is essential in the natural sciences, engineering, medicine, finance, computer science, and the social sciences. Although mathematics is extensively used for modeling phenomena, the fundamental truths of mathematics are independent of any scientific experimentation.
Jason Fitz and Frank Schwab join forces to give their instant reactions and takeaways to every game from Week 9 of NFL action. The duo start with highlighting the biggest games from Sunday ...
A branch of mathematics that studies change and has two major sub-fields: differential calculus (concerning rates of change and slopes of curves), and integral calculus (concerning accumulation of quantities and the areas under and between curves). These two branches are related to each other by the fundamental theorem of calculus.