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Numbers, Algebra, Discrete vs Continuous
Natural Numbers
Natural numbers are the whole numbers used for counting discrete quantities.
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Natural Numbers
Definition
Natural numbers are the whole numbers used for counting.
In this series, we use:
0, 1, 2, 3, 4, ...
Some contexts start natural numbers at 1.
For computation and counting empty collections, including 0 is useful.
Natural numbers = numbers for counting discrete quantities.
Counting Objects
Natural numbers answer questions like:
How many items?
How many steps?
How many nodes?
How many edges?
Examples:
0 files
1 input
3 nodes
10 steps
Natural numbers count things that come in separate units.
Natural Numbers Are Discrete
Natural numbers do not include values between whole counts.
Between:
2
3
there is no natural number.
You can have 2 nodes or 3 nodes, but not 2.5 nodes in a normal graph.
Natural numbers are separated, countable values.
Operations On Natural Numbers
Some operations stay inside natural numbers.
Example:
2 + 3 = 5
2 * 3 = 6
But subtraction may leave the natural numbers.
Example:
2 - 5 = -3
-3 is not a natural number.
Natural numbers are useful, but not closed under every operation.
Why Natural Numbers Matter
Natural numbers are the starting point for numerical structure.
They let us count:
- symbols
- states
- steps
- nodes
- edges
- possible choices
This makes them directly useful for computation and graph structure.
Counting is the first numerical layer on top of structure.
Final Summary
- Natural numbers are whole numbers used for counting.
- This series includes
0as a natural number. - Natural numbers are discrete.
- They count separate units.
- Addition and multiplication stay natural.
- Subtraction can leave the natural numbers.
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Continue the series.
Integers