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Numbers, Algebra, Discrete vs Continuous
Integers
Integers extend natural numbers by adding negative whole numbers.
~/writing/math-foundations-for-reasoning-models $ cat topic.md
Integers
Definition
Integers are whole numbers that include negatives, zero, and positives.
They look like:
..., -3, -2, -1, 0, 1, 2, 3, ...
Integers = whole numbers with direction around zero.
Why Integers Extend Natural Numbers
Natural numbers can count:
0, 1, 2, 3
But they cannot represent values below zero.
Integers allow:
-1
-2
-3
This matters when representing change, loss, debt, offset, or direction.
Integers let whole-number quantities move below zero.
Simple Examples
Examples of integer values:
temperature change: -5
account balance: -20
position offset: +3
counter value: 0
These values still move in whole steps.
They do not include fractions.
Integers are still discrete values.
Integers And Subtraction
Integers handle subtraction more naturally than natural numbers.
Example:
2 - 5 = -3
The result is not natural, but it is an integer.
Integers make subtraction closed over whole numbers.
Integers On A Number Line
Integers can be placed on a number line:
... -3 -2 -1 0 1 2 3 ...
Each neighboring integer is one step apart.
This makes integers useful for step-based movement.
Integers represent discrete positions around zero.
Final Summary
- Integers include negative whole numbers, zero, and positive whole numbers.
- Integers extend natural numbers.
- They are useful for change, direction, debt, and offset.
- Integers are discrete.
- Subtraction of integers stays inside integers.
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Continue the series.
Rational Numbers