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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.
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 category theory, a branch of mathematics, an initial object of a category C is an object I in C such that for every object X in C, there exists precisely one morphism I → X. The dual notion is that of a terminal object (also called terminal element): T is terminal if for every object X in C there exists exactly one morphism X → T.
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.
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 .
Rigor is a cornerstone quality of mathematics, and can play an important role in preventing mathematics from degenerating into fallacies. well-behaved An object is well-behaved (in contrast with being Pathological ) if it satisfies certain prevailing regularity properties, or if it conforms to mathematical intuition (even though intuition can ...
A mathematical object is an abstract concept arising in mathematics. [1] Typically, a mathematical object can be a value that can be assigned to a symbol, and therefore can be involved in formulas.