Mathematical definition of number?

Click For Summary
The discussion revolves around the lack of a clear mathematical definition for "number," with participants debating whether it should be defined as a member of a mathematical structure or a specific set like magmas. The complexity arises from the inclusion and exclusion of various types of numbers, such as cardinals, ordinals, and complex numbers, leading to the suggestion that the term "number" might be too ambiguous for precise mathematical discourse. Some argue that numbers are fundamental constructs derived from human experience, while others believe that sets provide a more foundational framework for understanding numbers. Ultimately, the conversation highlights the tension between intuitive understanding and formal definitions in mathematics, suggesting that the term "number" may remain inherently undefined yet useful in context.
  • #31
Yes, because you can't define "cardinality" until after you have the natural numbers.
 

Similar threads

  • · Replies 72 ·
3
Replies
72
Views
8K
  • · Replies 4 ·
Replies
4
Views
7K
  • · Replies 2 ·
Replies
2
Views
510
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 13 ·
Replies
13
Views
3K
  • · Replies 33 ·
2
Replies
33
Views
6K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 22 ·
Replies
22
Views
4K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 6 ·
Replies
6
Views
3K