Some articles on mathematical object, object, mathematical objects, objects, mathematical:
Mathematical Object
... A mathematical object is an abstract object arising in philosophy of mathematics and mathematics ... Commonly encountered mathematical objects include numbers, permutations, partitions, matrices, sets, functions, and relations ... Geometry as a branch of mathematics has such objects as hexagons, points, lines, triangles, circles, spheres, polyhedra, topological spaces and manifolds ...
... A mathematical object is an abstract object arising in philosophy of mathematics and mathematics ... Commonly encountered mathematical objects include numbers, permutations, partitions, matrices, sets, functions, and relations ... Geometry as a branch of mathematics has such objects as hexagons, points, lines, triangles, circles, spheres, polyhedra, topological spaces and manifolds ...
Philosophers Of Mathematics - Contemporary Schools of Thought - Structuralism
... Structuralism is a position holding that mathematical theories describe structures, and that mathematical objects are exhaustively defined by their places in such structures, consequently having no intrinsic ... Other examples of mathematical objects might include lines and planes in geometry, or elements and operations in abstract algebra ... epistemologically realistic view in that it holds that mathematical statements have an objective truth value ...
... Structuralism is a position holding that mathematical theories describe structures, and that mathematical objects are exhaustively defined by their places in such structures, consequently having no intrinsic ... Other examples of mathematical objects might include lines and planes in geometry, or elements and operations in abstract algebra ... epistemologically realistic view in that it holds that mathematical statements have an objective truth value ...
Mathematical Object - Foundational Paradoxes
... If, however, the goal of mathematical ontology is taken to be the internal consistency of mathematics, it is more important that mathematical objects be definable in some uniform way (for example, as sets ... higher priority than the faithful reflection of the details of mathematical practice as a justification for defining mathematical objects to be sets ... Much of the tension created by this foundational identification of mathematical objects with sets can be relieved without unduly compromising the goals of foundations by allowing two kinds of objects into the ...
... If, however, the goal of mathematical ontology is taken to be the internal consistency of mathematics, it is more important that mathematical objects be definable in some uniform way (for example, as sets ... higher priority than the faithful reflection of the details of mathematical practice as a justification for defining mathematical objects to be sets ... Much of the tension created by this foundational identification of mathematical objects with sets can be relieved without unduly compromising the goals of foundations by allowing two kinds of objects into the ...
Famous quotes containing the words objects and/or mathematical:
“I stand in the sunny noon of life. Objects no longer glitter in the dews of morning, neither are yet softened by the shadows of evening.”
—Margaret Fuller (1810–1850)
“What he loved so much in the plant morphological structure of the tree was that given a fixed mathematical basis, the final evolution was so incalculable.”
—D.H. (David Herbert)
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