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Encyclopedia: Without loss of generality

Without loss of generality (abbreviated to WLOG or WOLOG and less commonly stated as without any loss of generality) is a frequently used expression in mathematics. The term is used before an assumption in a proof which narrows the scope of analysis to some subset of possible instantiations of the premise; it is implied that the structure of the proof on this subset can be generalized to all others. Thus, through a subproof depending on a subset of the premise, we show that conclusions are proven to follow from the full premise.

Translations

How to say "Without loss of generality" in other languages:

	(German)	Ohne Beschränkung der Allgemeinheit
	(Spanish)	Sin pérdida de generalidad
	(French)	Sans perte de généralité

Search results

Screened Poisson equation

mesons and electric field screening in plasmas. Without loss of generality, we will take λ to be... for general f using the method of Green's functions. The Green's function G is defined by Assuming... Laplace operator, λ is a constant, and f is an arbitrary function of position (known as the "source...

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List of basic discrete mathematics topics

value Up to Normal form Canonical form Without loss of generality Vacuous truth Contradiction... This is a list of basic discrete mathematics topics , by Wikipedia page. Included here is much of.... This is not, however, intended as a complete glossary of mathematical terms; just a selection of...

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Random variable

, but without loss of generality they can be made into independent random variables on the same..., but without loss of generality they can be made into independent random variables on the same... concept of expected value of a random variable, denoted E[ X]. Note that in general, E[ f( X)] is not the...

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Fundamental theorem of arithmetic

products) violating our assumption. We can now assume without loss of generality that p 1 is a prime... prime factorizations are not known, the use of Euclid's algorithm generally requires much less...In mathematics, and in particular number theory, the fundamental theorem of arithmetic or unique...

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Principal components analysis

. Without loss of generality, assume X has zero empirical mean. We want to find a d × d orthonormal... that the greatest variance by any projection of the data set comes to lie on the first axis (then... can be used for reducing dimensionality in a dataset while retaining those characteristics of the...

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Rice's theorem

now assume that P (a ) is an algorithm that decides some non-trivial property of F a. Without loss... decides with generality non-trivial questions on the final behavior of computer programs. This is... algorithm for deciding any other nontrivial property of programs, and will be given in general below. The...

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Combinatorics

remaining 5 people, there must be at least three who either all know or all do not know A. Without loss of generality, assume three such people all know A. But then among those three people, at least two of.... More generally, given an infinite collection of finite sets { Si } typically indexed by the...

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Graph coloring

assignment of "colors" , almost always taken to be consecutive integers starting from 1 without loss of... glossary of graph theory. Vertex coloring When used without any qualification, a coloring of a graph... A 3-coloring suits this graph, but fewer colors would result in adjacent verticies of the same...

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Mathematics as a language

meanings, such as " if and only if ", " necessary and sufficient " and " without loss of generality... : What do we mean when we talk about the language of mathematics ? To what extent does mathematics meet generally accepted criteria of being a language ? A secondary question is : If it is valid to...

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Partial fraction decomposition over R

...

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