;
Learning starts with a question. Asking is a signal for knowledge request!
First time here? Checkout the FAQs!
x

*Math Image Search only works best with SINGLE, zoomed in, well cropped images of math. No selfies and diagrams please :)

0 like 0 dislike
186 views
In mathematics, what are surreal numbers?
in Mathematics by Platinum (102k points) | 186 views

1 Answer

0 like 0 dislike
Best answer
Surreal numbers are the most natural collection of numbers which includes both the real numbers and the infinite ordinal numbers of Georg Cantor. They were invented by John H. Conway in 1969. Every real number is surrounded by surreals, which are closer to it than any real number. Knuth (1974) describes the surreal numbers in a work of fiction.

The surreal numbers are written using the notation \(\{a \mid b\}\), where \(\{\mid\}=0,\{0 \mid\}=1\) is the simplest number greater than \(0,\{1 \mid\}=2\) is the simplest number greater than 1, etc. Similarly, \(\{\mid 0\}=-1\) is the simplest number less than 0 , etc. However, 2 can also be represented by \(\{1 \mid 3\},\{3 / 2 \mid 4\},\{1 \mid \omega\}\), etc.
Some simple games have abbreviated names that can be expressed in terms of surreal numbers. For example, \(*=\{0 \mid 0\}, 1=\{0 \mid\}\), \(n=\{n-1 \mid\}\) for an integer \(n, 1 / 2=\{0 \mid 1\}, \uparrow=\{0 \mid *\}\), and \(\downarrow=\{* \mid 0\}\). Most surreal numbers can be represented as hackenbush positions.

by Platinum (102k points)

Related questions

0 like 0 dislike
1 answer
asked Feb 4, 2022 in Mathematics by AstraNova Diamond (59.2k points) | 168 views
1 like 0 dislike
1 answer
asked Oct 26, 2022 in Mathematics by MathsGee Platinum (102k points) | 226 views
0 like 0 dislike
0 answers
asked Sep 7, 2022 in Mathematics by MathsGee Platinum (102k points) | 315 views
0 like 0 dislike
1 answer
0 like 0 dislike
1 answer
0 like 0 dislike
1 answer
0 like 0 dislike
1 answer
0 like 0 dislike
1 answer
0 like 0 dislike
0 answers
0 like 0 dislike
1 answer
asked Feb 6 in Mathematics by AstraNova Diamond (59.2k points) | 270 views
0 like 0 dislike
1 answer
asked Jan 27 in Mathematics by AstraNova Diamond (59.2k points) | 240 views
1 like 0 dislike
1 answer
0 like 0 dislike
0 answers
asked Jan 11, 2022 in Mathematics by MathsGee Platinum (102k points) | 212 views
0 like 0 dislike
1 answer

Join MathsGee Q&A, where you get instant answers to your questions from our AI, AstraNova and verified by human experts. We use a combination of generative AI and human experts to provide you the best solutions to your problems.

On the MathsGee Q&A, you can:

1. Get instant answer to your questions

2. Convert image to latex

3. AI-generated answers and insights

4. Get expert-verified answers

5. Vote on questions and answers

6. Tip your favorite community members

7. Join expert live video sessions (Paid/Free)

8. Earn points by participating

9. Take a course

10. Enjoy our interactive learning resources


Posting on the MathsGee Q&A

1. Remember the human

2. Act like you would in real life

3. Find original source of content

4. Check for duplicates before publishing

5. Read the community guidelines


MathsGee Q&A Rules

1. Answers to questions will be posted immediately after moderation

2. Questions will be queued for posting immediately after moderation

3. Depending on the number of messages we receive, you could wait up to 24 hours for your message to appear. But be patient as posts will appear after passing our moderation.


MathsGee Q&A


Acalytica


Social Proof


Web Analytics


Courses