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In mathematics, more precisely in measure theory, an atom is a measurable set that has positive measure and contains no set of smaller positive measures. A measure that has no atoms is called non-atomic or atomless .
Nonterminal symbols are those symbols that can be replaced. They may also be called simply syntactic variables.A formal grammar includes a start symbol, a designated member of the set of nonterminals from which all the strings in the language may be derived by successive applications of the production rules.
Mathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of ...
In the mathematical field of order theory, an element a of a partially ordered set with least element 0 is an atom if 0 < a and there is no x such that 0 < x < a. Equivalently, one may define an atom to be an element that is minimal among the non-zero elements, or alternatively an element that covers the least element 0 .
The ordered field of real algebraic numbers is the unique atomic model of the theory of real closed fields.; Any finite model is atomic. A dense linear ordering without endpoints is atomic.
3. Between two groups, may mean that the first one is a proper subgroup of the second one. > (greater-than sign) 1. Strict inequality between two numbers; means and is read as "greater than". 2. Commonly used for denoting any strict order. 3. Between two groups, may mean that the second one is a proper subgroup of the first one. ≤ 1.
In mathematics, more specifically ring theory, an atomic domain or factorization domain is an integral domain in which every non-zero non-unit can be written in at least one way as a finite product of irreducible elements.
In mathematical logic, a literal is an atomic formula (also known as an atom or prime formula) or its negation. [1] [2] The definition mostly appears in proof theory (of classical logic), e.g. in conjunctive normal form and the method of resolution. Literals can be divided into two types: [2] A positive literal is just an atom (e.g., ).