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The bandwagon effect is a psychological phenomenon where people adopt certain behaviors, styles, or attitudes simply because others are doing so. [1] More specifically, it is a cognitive bias by which public opinion or behaviours can alter due to particular actions and beliefs rallying amongst the public. [ 2 ]
Because the algebraic numbers form a subfield of the real numbers, many irrational real numbers can be constructed by combining transcendental and algebraic numbers. For example, 3 π + 2, π + √ 2 and e √ 3 are irrational (and even transcendental).
Bandwagon effect, "copycat" behavior Argumentum ad populum, or the bandwagon fallacy: "If many believe so, it is so" Bandwagon fan, a person who likes a sport team just because of their recent success. Example: Sergei Respublicanschii; Bandwagoning, a term in international relations
In mathematics, an irrational number is any real number that is not a rational number, i.e., one that cannot be written as a fraction a / b with a and b integers and b not zero. This is also known as being incommensurable, or without common measure. The irrational numbers are precisely those numbers whose expansion in any given base (decimal ...
Rational numbers have irrationality exponent 1, while (as a consequence of Dirichlet's approximation theorem) every irrational number has irrationality exponent at least 2. On the other hand, an application of Borel-Cantelli lemma shows that almost all numbers, including all algebraic irrational numbers , have an irrationality exponent exactly ...
In his Essai sur la théorie des nombres (1798), Adrien-Marie Legendre derives a necessary and sufficient condition for a rational number to be a convergent of the simple continued fraction of a given real number. [4] A consequence of this criterion, often called Legendre's theorem within the study of continued fractions, is as follows: [5 ...
A Perfect Example of Irrational Exuberance. Alex Planes, The Motley Fool. Updated July 14, 2016 at 9:42 PM. ... "In this world nothing can be said to be certain, except death and taxes." He penned ...
The powers of two whose exponents are powers of two, , form an irrationality sequence.However, although Sylvester's sequence. 2, 3, 7, 43, 1807, 3263443, ... (in which each term is one more than the product of all previous terms) also grows doubly exponentially, it does not form an irrationality sequence.