# Category:Ordering on Natural Numbers

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This category contains results about **Ordering on Natural Numbers**.

Definitions specific to this category can be found in Definitions/Ordering on Natural Numbers.

Let $\N$ denote the natural numbers.

The ordering on $\N$ is the relation $\le$ everyone is familiar with.

For example, we use it when we say:

- James has $6$ apples, which is more than Mary, who has $4$.

which can be symbolised as:

- $6 \ge 4$

## Subcategories

This category has the following 3 subcategories, out of 3 total.

## Pages in category "Ordering on Natural Numbers"

The following 14 pages are in this category, out of 14 total.

### M

### N

- Natural Number Less than or Equal to Successor of Another
- Natural Number m is Less than n iff m is an Element of n
- Natural Number m is Less than n implies n is not Greater than Successor of n
- Natural Number Ordering is Preserved by Successor Mapping
- Natural Numbers are Comparable
- Negation of Ordering of Natural Numbers is Provable
- No Natural Number between Number and Successor
- Non-Empty Bounded Subset of Natural Numbers has Greatest Element
- Non-Empty Finite Set of Natural Numbers has Greatest Element