ordinal-number 0.2

A package to use OrdinnalNumber

This package is for ordinal numbers. Ordered numbers are a concept from set theory that extends the natural numbers to compare the "length" of aligned sets. This library implements ordered numbers: sum, difference (left-hand inverse), product, quotient (left-hand inverse), truncation, division, remainder, comparison of sizes, square root, etc. If I have enough power, I will also create "log", "n-square root" and "factorial". If requested, I will make others. (my Email:alphagameplayerpro$gmail.com (please replace $ to @))

And,

```

omega = ordinal_number.OMEGA

```

at the beginning of the program. That way, it is intuitive and the output of repr() can be executed as is.





References

http://www.behounek.online/logic/papers/ordcalc/index.html

https://proofwiki.org/wiki/Division_Theorem_for_Ordinals#Existence_of_%7F'%22%60UNIQ-MathJax-9-QINU%60%22'%7F_and_%7F'%22%60UNIQ- MathJax-10-QINU%60%22'%7F

https://manabitimes.jp/math/1318 (Japanese site)



examples



improt ordinal-number as ord



omega = ord.OMEGA



#__add__

omega+1+omega+omega+1

#>>> omega*2+1



#__sub__  A-B := (X such that B+X=A) if not exists, return None

(omrga**2*2+omega*2+1)-omega**2

#>>> omega**2+omega*2+1

(omega*2+1)-omega**2

#>>> None



#__mul__

(omega+1)*(omega+1)

#>>> omega**2+omega+1



#__truediv__  A/B := (X such that B*X=A) if not exists, return None

(omega**2+omega+1)/(omega+1)

#>>> omega+1

(omega**2+omega+1)/omega

#>>> None



#__floordiv__  A//B := (X such that B*X+Y=A ,0<=Y<B)

(omega**2+omega+1)//(omega+1)

#>>> omega+1

(omega**2+omega+1)//omega

#>>> omega+1



#__truediv__  A%B := (Y such that B*X+Y=A ,0<=Y<B)

(omega**2+omega+1)%(omega+1)

#>>> 0

(omega**2+omega+1)%omega

#>>> 1



#__pow__

(omega+1)**2

#>>> omega**2+omega+1

2**omega

#>>> omega

omega**2

#>>> omega



#sqrt(self)

(omega**2+omega+1).sqrt()

#>>> omega+1