数学对象

数学对象（Mathematical object）是数学中的抽象概念。用数学的普通语言来说，对象是任何可以或已经用演绎推理和数学证明正式定义的对象。一般地，一个数学对象可以是一个能代入变数的值，从而可以用于公式里。 经常遇到的数学对象包括数、集合、函数、表示式、几何形状、其他数学对象的变换和空间。数学对象可以非常复杂。比如说，定理、证明甚至理论在证明论中被视为数学对象。

四维超立方体的施莱格尔图

数学对象的存在是数学哲学家进行大量研究和讨论的对象。[1]

按分支分类的数学对象列表

参见

参考文献

  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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