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In mathematics, a structure on a set (or on some sets) refers to providing it (or them) with certain additional features (e.g. an operation, relation, metric, or topology). Τhe additional features are attached or related to the set (or to the sets), so as to provide it (or them) with some additional meaning or significance.
A definition of "matter" based on its physical and chemical structure is: matter is made up of atoms. [17] Such atomic matter is also sometimes termed ordinary matter. As an example, deoxyribonucleic acid molecules (DNA) are matter under this definition because they are made of atoms.
A structure on a set, or more generally a type, consists of additional mathematical objects that in some manner attach (or are related) to the set, making it easier to visualize or work with, or endowing the collection with meaning or significance.
In crystallography, crystal structure is a description of ordered arrangement of atoms, ions, or molecules in a crystalline material. [1] Ordered structures occur from intrinsic nature of constituent particles to form symmetric patterns that repeat along the principal directions of three-dimensional space in matter.
Second, a mathematical structure may have more than one definition (for example, topological space has at least seven definitions; ordered field has at least two definitions). In the former case, equivalence of two definitions means that a mathematical object (for example, geometric body) satisfies one definition if and only if it satisfies the ...
Logicism asserts that all mathematical truths can be reduced to logical truths, and all objects forming the subject matter of those branches of mathematics are logical objects. In other words, mathematics is fundamentally a branch of logic , and all mathematical concepts, theorems , and truths can be derived from purely logical principles and ...
Tegmark's MUH is the hypothesis that our external physical reality is a mathematical structure. [3] That is, the physical universe is not merely described by mathematics, but is mathematics — specifically, a mathematical structure. Mathematical existence equals physical existence, and all structures that exist mathematically exist physically ...
Chemistry is the scientific study of the properties and behavior of matter. [1] It is a physical science within the natural sciences that studies the chemical elements that make up matter and compounds made of atoms, molecules and ions: their composition, structure, properties, behavior and the changes they undergo during reactions with other substances.