Any numbers being Complex numbers

Click For Summary

Discussion Overview

The discussion revolves around the classification of numbers, specifically whether any numbers exist that are not considered subsets of complex numbers, represented as a + bi, where a and b are real numbers. The scope includes conceptual clarifications and definitions related to different types of numbers in mathematics.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions if there are any numbers that do not fit within the complex number framework defined as a + bi.
  • Another participant challenges the definition of "number," suggesting that the term is too broad and encompasses various types such as real numbers, transfinite numbers, p-adic numbers, and hyperreal numbers, which may not have clear relationships.
  • A different participant references information from Wikipedia, noting that sets of numbers not considered subsets of complex numbers are sometimes referred to as hypercomplex numbers, suggesting this might be relevant to the original question.
  • Another contribution states that numerical quantities described with vectors of more than two elements or tensors generally cannot be classified as complex numbers.

Areas of Agreement / Disagreement

Participants express differing views on the definition and classification of numbers, indicating that multiple competing perspectives remain without a clear consensus.

Contextual Notes

The discussion highlights the ambiguity in the definition of "number" and the potential limitations in understanding the relationships between different types of numbers, including complex and hypercomplex numbers.

Anachronistic
Messages
8
Reaction score
1
Are there any numbers that is not considered to be a subset of a complex number subset of

a + bi

Where a and b are real numbers?
 
Physics news on Phys.org
Define "number".

I'm asking because the concept of number is not well-defined in mathematics. There are a lot of things which carry the name "number", like real number, transfinite number, p-adic number, hyperreal number, etc. All these things are called numbers and often have no obvious relationship to each other. The concept of a number is too broad. It is not defined in mathematics.
 
Last edited:
I don't know as much as micromass on this subject, but I just read this on wikipedia and I think it might interest the OP.

On the wiki page of Number, it says under the header "Complex Numbers" the following:
Sets of numbers that are not subsets of the complex numbers are sometimes called hypercomplex numbers.
which is the same wording at the OP used, so maybe he chould check out hypercomplex numbers.
 
Numerical quantities described with vectors of more than two elements or tensors cannot, as a general rule, be described as complex numbers.
 

Similar threads

Undergrad Erroneously finding discrepancy in transpose rule
  • · Replies 13 ·
Replies
13
Views
2K
MHB Is z + z¯ and z × z¯ Real for Any Complex Number z?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Is Complex Differentiation Defined for Linear Transformations?
  • · Replies 4 ·
Replies
4
Views
1K
Undergrad Visualization of complex vectors and dot product
  • · Replies 14 ·
Replies
14
Views
5K
Undergrad Quintic Polynomial Tschirnhaus Transform: Possible complex Bring Radicals
  • · Replies 0 ·
Replies
0
Views
3K
MHB Are Non-Ordered Numbers More Than Complex Numbers?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Anti-dual numbers and what are their properties?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Complex number and split complex number
  • · Replies 3 ·
Replies
3
Views
2K
Graduate How Does U(1) Double-Cover SO(2) for a Specified Angle?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Fourier Transformation on a Ring
  • · Replies 11 ·
Replies
11
Views
3K