What are surreal numbers and how do they work?

In summary, the concept being discussed is Conway's surreal numbers, which are a type of number invented by mathematician John Horton Conway. They have various applications in mathematics and can be notated and expanded to infinities and infinitesimals. Detailed information can be found in Conway's book, "Numbers and Games."
  • #1
Aakash Lakshmanan
9
0
Hey guys! I have heard of this concept in various places and sort of understands what it attempts to do. Can anybody please explain it to me in more detail like how it works, how to notate it, and how to expand it to infinities and infinitesimals. Thanks in advance!

Aakash Lakshmanan
xphysx.com - a repository of cool physics (and math)
 
Physics news on Phys.org
  • #3
Aakash Lakshmanan said:
Hey guys! I have heard of this concept in various places and sort of understands what it attempts to do. Can anybody please explain it to me in more detail like how it works, how to notate it, and how to expand it to infinities and infinitesimals. Thanks in advance!

Aakash Lakshmanan
xphysx.com - a repository of cool physics (and math)

Hello, you can find detailed information at: https://www.whitman.edu/Documents/Academics/Mathematics/Grimm.pdf
 
  • #4
Aakash Lakshmanan said:
Hey guys! I have heard of this concept in various places and sort of understands what it attempts to do. Can anybody please explain it to me in more detail like how it works, how to notate it, and how to expand it to infinities and infinitesimals. Thanks in advance!

Aakash Lakshmanan
xphysx.com - a repository of cool physics (and math)
Conway invented them and his little book, "Numbers and Games(?)" is terrific.
 

1. What are surreal numbers?

Surreal numbers are a type of number system that was introduced by mathematician John Conway in 1974. They are a way of extending the real numbers to include infinite and infinitesimal quantities, allowing for more complex mathematical operations and calculations.

2. How are surreal numbers different from real numbers?

Surreal numbers are different from real numbers in that they include numbers that are infinitely large and infinitely small. Real numbers are limited to finite quantities, while surreal numbers allow for numbers that are greater than or less than any real number.

3. How are surreal numbers represented?

Surreal numbers are represented using a notation that consists of two parts, known as the left and right sets. These sets contain all of the numbers that are smaller and larger than the number in question, respectively. This notation allows for the representation of infinitely large and small numbers.

4. What is the significance of surreal numbers?

Surreal numbers have several applications in mathematics, including in the study of games and game theory, as well as in the analysis of complex systems. They also provide a way to better understand and analyze infinity and infinitesimal quantities, which are often encountered in advanced mathematics.

5. Can surreal numbers be used in everyday life?

While surreal numbers have many applications in theoretical mathematics, they are not commonly used in everyday life. Real numbers are usually sufficient for most practical calculations and applications. However, surreal numbers can provide a deeper understanding of mathematical concepts and may have future applications in fields such as computer science and economics.

Similar threads

  • Set Theory, Logic, Probability, Statistics
Replies
13
Views
2K
Replies
4
Views
1K
Replies
2
Views
1K
  • STEM Academic Advising
Replies
10
Views
2K
  • Set Theory, Logic, Probability, Statistics
3
Replies
93
Views
16K
  • Special and General Relativity
Replies
1
Views
566
Replies
14
Views
1K
Replies
2
Views
961
Back
Top