Not Complex Numbers: Are There Any Other Options?

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SUMMARY

The discussion centers on the concept of "numbers" in mathematics, highlighting that the term is often misused and lacks a definitive definition. It identifies various types of numbers, including rational numbers, real numbers, complex numbers, p-adic numbers, transfinite numbers, hyperreal numbers, surreal numbers, and supernatural numbers. The conversation emphasizes that the classification of these entities as "numbers" is subjective and varies based on context. Ultimately, the term "numbers" is overloaded and does not convey a singular meaning in mathematical discourse.

PREREQUISITES
  • Understanding of basic mathematical concepts, including rational and real numbers.
  • Familiarity with complex numbers and their properties.
  • Knowledge of advanced mathematical constructs such as p-adic numbers and transfinite numbers.
  • Awareness of the philosophical implications of mathematical terminology.
NEXT STEPS
  • Research the properties and applications of quaternions in mathematics.
  • Explore the definitions and implications of hyperreal and surreal numbers.
  • Study the concept of p-adic numbers and their significance in number theory.
  • Investigate the philosophical aspects of mathematical terminology and its impact on understanding mathematical concepts.
USEFUL FOR

Mathematicians, educators, students of mathematics, and anyone interested in the philosophical and theoretical foundations of numerical classifications.

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Are there any numbers in mathematics that are not complex numbers?
 
Mathematics news on Phys.org
Quaternions?
 
There are no such things as "numbers" in mathematics. It is a term that is used and abused a lot. We have

- Rational numbers
- Real numbers
- Complex numbers
- p-adic numbers
- Transfinite numbers
- Hyperreal numbers
- Surreal numbers
- Supernatural numbers
- etc.

Some of these things are not what you have in mind when you talk about numbers, but they're called numbers anyway. The term numbers is overloaded and doesn't have any real meaning: there is no definition to determine whether something is a number or not.
 

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