Lectures on the Philosophy of MathematicsOpen court publishing Company, 1918 - 206 σελίδες |
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Σελίδα 9
... entities , and operations upon them . By system is meant any aggregation of mathematical entities which has sense , either consistent or inconsistent . These descriptions will become more definite in the de- tailed study of the ...
... entities , and operations upon them . By system is meant any aggregation of mathematical entities which has sense , either consistent or inconsistent . These descriptions will become more definite in the de- tailed study of the ...
Σελίδα 20
... entities - the ratios - that we have created . This is a real identification , for we can easily conclude , by carefully considering the matter , that multiplication , as 3 by 4 , for example , is only illustrated by the arrangement of ...
... entities - the ratios - that we have created . This is a real identification , for we can easily conclude , by carefully considering the matter , that multiplication , as 3 by 4 , for example , is only illustrated by the arrangement of ...
Σελίδα 22
... entity already in the universe is not explainable in terms of integers , and the Pythagorean theory of the numerical structure of the universe breaks down , although much of the modern physics might be so construed as to restore this ...
... entity already in the universe is not explainable in terms of integers , and the Pythagorean theory of the numerical structure of the universe breaks down , although much of the modern physics might be so construed as to restore this ...
Σελίδα 38
... entity con- sisting of a multiplex of two or more numbers instead of one number ; or in the language of functions , a manifold is a range for functions of two or many variables . A point in a plane is a duplex of two variables , x and y ...
... entity con- sisting of a multiplex of two or more numbers instead of one number ; or in the language of functions , a manifold is a range for functions of two or many variables . A point in a plane is a duplex of two variables , x and y ...
Σελίδα 48
... entities . Indeed , from this point of view we could define mathematics as the subject whose problem was the determination of the ways of building up stable combinations of assigned elements under given rules called postulates . A book ...
... entities . Indeed , from this point of view we could define mathematics as the subject whose problem was the determination of the ways of building up stable combinations of assigned elements under given rules called postulates . A book ...
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algebraic equations Amer analysis applied arithmetic arrangements assert branch of mathematics calculus calculus of classes called century character combinations complex numbers consider consists constructions continuous continuous functions created creation deductions define definite differential equations division domain elements Encyclopédie ensemble entities Euclidean geometry example existence finite four-dimensional fraction geometry given hypercomplex hypernumbers idea ideal imaginary infinite infinity instance integers intuition invariants invention investigation irrational numbers isomorphic laws logic logistic magic squares mathe mathematician mathématiques matics method mind nature negative numbers Non-Euclidean Geometry notion objects operations Pascal's theorem philosophy philosophy of mathematics physics plane Poincaré possible postulates problems processes projective geometry properties propositional function quaternions range rational numbers reality reduce relations roots solutions space structure symbols theorems theory of equations theory of functions theory of numbers things tion transformations true truth universe variables vector