### Some articles on *axioms, axiom*:

Scale-space

... for choosing a particular type of scale space representation is to establish a set of scale-space

**Axioms**... for choosing a particular type of scale space representation is to establish a set of scale-space

**axioms**, describing basic properties of the desired scale-sp ... Once established, the**axioms**narrow the possible scale-space representations to a smaller class, typically with only a few free parameters ... A set of standard scale space**axioms**, discussed below, leads to the linear Gaussian scale-space, which is the most common type of scale space used in image processing and computer vision ...Brouwer–Hilbert Controversy - Deeper Philosophic Differences - A Philosophical Defeat in The Quest For "truth" in The Choice of

... And at least with respect to his choice of

**Axioms**... And at least with respect to his choice of

**axioms**the case can be made that indeed he does eschew the notion ... issue is just how does one choose "the**axioms**"? Until Hilbert proposed his formalism, the**axioms**were chosen on an "intuitive" (experiential) basis ... The primitive form of the induction**axiom**is another – if a predicate P(n) is true for n = 0 and if for all natural numbers n it is true that P(n) => P(n+1), then P(n) is ...Tarski's High School Algebra Problem - Statement of The Problem

... Tarski considered the following eleven

... Tarski considered the following eleven

**axioms**about addition ('+'), multiplication ('·'), and exponentiation to be standard**axioms**taught in high school x + y = y + x (x + y) + z = x + (y + z) x ... These eleven**axioms**, sometimes called the high school identities, are related to the**axioms**of an exponential ring ... that are true for all positive integers, but that cannot be proved using only the**axioms**1–11? ...Statistical Proof -

... There are two kinds of

**Axioms**... There are two kinds of

**axioms**, 1) conventions that are taken as true that should be avoided because they cannot be tested, and 2) hypotheses ... Proof in the theory of probability was built on four**axioms**developed in the late 17th century The probability of a hypotheses is a non-negative real number The probability of necessary truth equals one ... The preceding**axioms**provide the statistical proof and basis for the laws of randomness, or objective chance from where modern statistical theory has ...Median Algebra

... median algebra is a set with a ternary operation satisfying a set of

... median algebra is a set with a ternary operation satisfying a set of

**axioms**which generalise the notion of median or majority function, as a Boolean function ... The**axioms**are The second and third**axioms**imply commutativity it is possible (but not easy) to show that in the presence of the other three,**axiom**(3) is redundant ... The fourth**axiom**implies associativity ...### Famous quotes containing the word axioms:

““I tell you the solemn truth that the doctrine of the Trinity is not so difficult to accept for a working proposition as any one of the *axioms* of physics.””

—Henry Brooks Adams (1838–1918)

“The *axioms* of physics translate the laws of ethics. Thus, “the whole is greater than its part;” “reaction is equal to action;” “the smallest weight may be made to lift the greatest, the difference of weight being compensated by time;” and many the like propositions, which have an ethical as well as physical sense. These propositions have a much more extensive and universal sense when applied to human life, than when confined to technical use.”

—Ralph Waldo Emerson (1803–1882)

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