Looking for help trying to understand surreals

[Mathematical]

My goal: Write a python script that will hold the left set, right set, and calculate the value of a surreal (if it is finite) and return it when called.

 

As I understand it, a surreal number [latex]S[/latex] and [latex]S'[/latex] are equvalent so long as the the maximum of the left sets, and the minimum of the left sets are the same

 

or simply: [latex]S=\{S_L|S_R\} \equiv \{max(S_L)|min(S_R)\} = S')[/latex]

 

 

[i cut everything else out, because I wasn't making sense, please see below]

 

 

For fuck's sake, I hate this unnecessarily complicated recursive numeral system. THIS is why more people don't understand surreals, because the numbering system isn't intuitive at all. Can someone please tell me how I can find the value of a given [latex]S[/latex]?

 

---

    def calcvalue(self):
        if self.rightisempty and self.leftisempty:
            return 0
        elif self.rightisempty:
            return max(self.left)+1
        elif self.leftisempty:
            return min(self.right_-1)
        else:
            return (max(left)+min(right))/2

Also here's this code. Is this accurate?

Edited February 5, 2017 by Mathematical

[wtf]

For fuck's sake, I hate this unnecessarily complicated recursive numeral system. THIS is why more people don't understand surreals, because the numbering system isn't intuitive at all. Can someone please tell me how I can find the value of a given [latex]S[/latex]?

What an interesting project. I just had a look at the Wiki page for the surreals to refresh my memory, and got confused pretty fast. Then I read through the Talk page. https://en.wikipedia.org/wiki/Talk:Surreal_number

 

There you'll find several experts in the subject arguing about how to define the surreals, what their properties are, whether the definition is circular, whether the surreals are the largest ordered field or not, whether they can properly be called a linear continuum. It's really worth reading. It's totally clear now why these aren't more well known. Even the pros aren't quite sure what they are.

Edited February 6, 2017 by wtf

[imatfaal]

Have you read Winning Ways by Berlekamp Conway and Guy - it is a good intro to Conway Games (Combinatorial Game Theory); I tried it - but whoosh so far over my head. I find wikipedia to be a less than good resource for stuff like this - scholarpedia is brilliant if the subject is covered, and eric weistien's mathworld on wolfram.com is terse but beautifully put together and well referenced.