The invariant set postulate concerns the possible relationship between fractal geometry and quantum mechanics and in particular the hypothesis that the...

invariant. Many cardinal invariants have been studied, and the relationships between them are often complex and related to axioms of set theory. Set-theoretic...

An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments...

the fabric of space itself is fractal, however. Physics portal Invariant set postulate Large-scale structure of the Universe Scale invariance Shape of...

interpretation Double-slit experiment Einstein's thought experiments Invariant set postulate Quantum eraser Schrödinger's cat Uncertainty principle Wheeler's...

system postulate (tensor product postulate) can be derived from the state postulate (Postulate I) and the measurement postulates (Postulates II); Moreover...

set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. One of those is the parallel postulate which...

the theory is presented as being based on just two postulates: The laws of physics are invariant (identical) in all inertial frames of reference (that...

radiation). The second postulate can be used to imply a stronger version of itself, namely that the spacetime interval is invariant under changes of inertial...

of fundamental physics, promoting the synergistic "Cosmological Invariant Set Postulate" as a primitive geometric principle for physics of the large and...

invariant theory, an invariant of a binary form is a polynomial in the coefficients of a binary form in two variables x and y that remains invariant under...

of the elements of the set.[citation needed] This can be considered the central postulate of musical set theory. In practice, set-theoretic musical analysis...

smooth families of operations (Lie groups). Formally, the Lagrangian is invariant under these transformations. The term "gauge" refers to any specific mathematical...

bring it into accordance with the postulate of relativity. While discussing various hypotheses on Lorentz invariant gravitation, he introduced the innovative...

have a rich set of invariants, coming from point-set topology, classic algebraic topology, and geometric topology. The most familiar invariants, which are...

playing this file? See media help. Invariant formations are also the side effect of derived rows where a segment of a set remains similar or the same under...

the strain tensors) has three independent invariant quantities associated with it. One set of such invariants are the principal stresses of the stress...

of physical principles, ranging from Maxwell's equations to Einstein's postulates of special relativity, and mathematical tools, spanning from elementary...

In mathematical physics, de Sitter invariant special relativity is the speculative idea that the fundamental symmetry group of spacetime is the indefinite...

ff) calls them "Peano's Postulates" and begins with "1.  0 is a natural number." Halmos (1960, p. 46) uses the language of set theory instead of the language...

sides are equal in length, then the triangles are congruent. The ASA postulate is attributed to Thales of Miletus. In most systems of axioms, the three...

Euclid's Elements contained five postulates that form the basis for Euclidean geometry. One of these, the parallel postulate, has been the subject of debate...

synthetic geometry similar to Euclidean geometry but without the parallel postulate. Abstract algebra The part of algebra devoted to the study of algebraic...

exists is Wallis's postulate and is logically equivalent to Euclid's parallel postulate. In hyperbolic geometry (where Wallis's postulate is false) similar...

to the Dehn plane) is external, and in this limited plane the parallel postulate is violated. For example, any line passing through the point (0, 1) on...

anticommutativity between spacelike separated fields. They also postulate the existence of a Poincaré-invariant state called the vacuum and demand it to be unique...

Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: For any given line R and point...

are Lebesgue measurable; examples of such sets include the Vitali set, and the non-measurable sets postulated by the Hausdorff paradox and the Banach–Tarski...

mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared...

mechanics. The theory is based on two postulates: (1) that the mathematical forms of the laws of physics are invariant in all inertial systems; and (2) that...