# Category:Ordinal Arithmetic

Jump to navigation
Jump to search

This category contains results about Ordinal Arithmetic.

Definitions specific to this category can be found in Definitions/Ordinal Arithmetic.

## Subcategories

This category has only the following subcategory.

## Pages in category "Ordinal Arithmetic"

The following 62 pages are in this category, out of 62 total.

### C

### F

### I

### L

### M

### O

- Ordinal Addition by One
- Ordinal Addition by Zero
- Ordinal Addition is Associative
- Ordinal Addition is Closed
- Ordinal Addition is Left Cancellable
- Ordinal Exponentiation is Closed
- Ordinal Exponentiation of Terms
- Ordinal Exponentiation via Cantor Normal Form/Corollary
- Ordinal Exponentiation via Cantor Normal Form/Limit Exponents
- Ordinal is Less than Ordinal times Limit
- Ordinal is Less than Ordinal to Limit Power
- Ordinal is Less than Sum
- Ordinal is Member of Ordinal Class
- Ordinal Multiplication by One
- Ordinal Multiplication by Zero
- Ordinal Multiplication is Associative
- Ordinal Multiplication is Closed
- Ordinal Multiplication is Left Cancellable
- Ordinal Multiplication is Left Distributive
- Ordinal Multiplication via Cantor Normal Form/Infinite Exponent
- Ordinal Multiplication via Cantor Normal Form/Limit Base
- Ordinal Power of Power
- Ordinal Subtraction when Possible is Unique
- Ordinal Sum of Powers
- Ordinals have No Zero Divisors
- Ordinals under Addition form Monoid
- Ordinals under Addition form Ordered Monoid
- Ordinals under Addition form Ordered Semigroup
- Ordinals under Addition form Semigroup
- Ordinals under Multiplication form Monoid
- Ordinals under Multiplication form Ordered Monoid
- Ordinals under Multiplication form Ordered Semigroup
- Ordinals under Multiplication form Semigroup

### S

- Subset is Compatible with Ordinal Addition
- Subset is Compatible with Ordinal Multiplication
- Subset is Left Compatible with Ordinal Addition
- Subset is Left Compatible with Ordinal Multiplication
- Subset is Right Compatible with Ordinal Addition
- Subset is Right Compatible with Ordinal Exponentiation
- Subset is Right Compatible with Ordinal Multiplication