数学对象

數學對象(Mathematical object)是数学中的抽象概念。用數學的普通語言來說,對象是任何可以或已經用演绎推理数学证明正式定義的物件。一般地,一個數學對象可以是一個能代入变数的值,從而可以用於公式裡。 經常遇到的數學對象包括集合函数表示式几何形状、其他數學對象的变换空间。數學對象可以非常複雜。比如說,定理证明甚至理论证明论中被視為數學對象。

數學對象的存在是數學哲學家進行大量研究和討論的對象。[1]

按分支分類的數學對象列表编辑

參見编辑

參考文獻编辑

  1. ^ Burgess, John, and Rosen, Gideon, 1997. A Subject with No Object: Strategies for Nominalistic Reconstrual of Mathematics. Oxford University Press. ISBN 0198236158
  • Azzouni, J., 1994. Metaphysical Myths, Mathematical Practice. Cambridge University Press.
  • Burgess, John, and Rosen, Gideon, 1997. A Subject with No Object. Oxford Univ. Press.
  • Davis, Philip and Reuben Hersh, 1999 [1981]. The Mathematical Experience. Mariner Books: 156–62.
  • Gold, Bonnie, and Simons, Roger A., 2011. Proof and Other Dilemmas: Mathematics and Philosophy页面存档备份,存于互联网档案馆. Mathematical Association of America.
  • Hersh, Reuben, 1997. What is Mathematics, Really?  Oxford University Press.
  • Sfard, A., 2000, "Symbolizing mathematical reality into being,  Or how mathematical discourse and mathematical objects create each other," in Cobb, P., et al., Symbolizing and communicating in mathematics classrooms:  Perspectives on discourse, tools and instructional design. Lawrence Erlbaum.
  • Stewart Shapiro, 2000. Thinking about mathematics: The philosophy of mathematics.  Oxford University Press.

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