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Bennett's inequality, an upper bound on the probability that the sum of independent random variables deviates from its expected value by more than any specified amount Bhatia–Davis inequality , an upper bound on the variance of any bounded probability distribution
Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
The feasible regions of linear programming are defined by a set of inequalities. In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. [1] It is used most often to compare two numbers on the number line by their size.
The first of these quadratic inequalities requires r to range in the region beyond the value of the positive root of the quadratic equation r 2 + r − 1 = 0, i.e. r > φ − 1 where φ is the golden ratio. The second quadratic inequality requires r to range between 0 and the positive root of the quadratic equation r 2 − r − 1 = 0, i.e. 0 ...
Many easily stated number problems have solutions that require sophisticated methods, often from across mathematics. A prominent example is Fermat's Last Theorem . This conjecture was stated in 1637 by Pierre de Fermat, but it was proved only in 1994 by Andrew Wiles , who used tools including scheme theory from algebraic geometry , category ...
Since the inequality dim(V 1 ∩V 2 ∩V 3 ∩V 4) ≤ dim(V 3 ∩V 4) holds, we have finished with the proof.♣ Proof (Ingleton's inequality): Suppose that M is a representable matroid and let A = [v 1 v 2 … v n] be a matrix such that M = M(A).
Standard Roman numerals do not have a symbol for 0; instead, nulla (or the genitive form nullae) from nullus, the Latin word for "none", was employed to denote a 0 value. [15] The first systematic study of numbers as abstractions is usually credited to the Greek philosophers Pythagoras and Archimedes. Some Greek mathematicians treated the ...
Economic inequality is an umbrella term for a) income inequality or distribution of income (how the total sum of money paid to people is distributed among them), b) wealth inequality or distribution of wealth (how the total sum of wealth owned by people is distributed among the owners), and c) consumption inequality (how the total sum of money spent by people is distributed among the spenders).