# Category:Ordinal Arithmetic

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This category contains results about **Ordinal Arithmetic**.

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

## Subcategories

This category has the following 2 subcategories, out of 2 total.

## Pages in category "Ordinal Arithmetic"

The following 60 pages are in this category, out of 60 total.

### C

### F

### I

### L

### M

### O

- 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 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