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Numbers, Algebra, Discrete vs Continuous
Discrete Values
Discrete values are separate, countable possibilities.
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Discrete Values
Definition
Discrete values are separate, countable possibilities.
Examples:
0, 1, 2, 3
true, false
red, green, blue
state A, state B, state C
Discrete value = one distinct option among separate possibilities.
Separate Choices
Discrete values come in distinct units.
Example:
number of nodes = 4
The next possible count is:
5
There is no normal count of:
4.5 nodes
Discrete values have gaps between valid possibilities.
Discrete Does Not Mean Numeric Only
Discrete values can be numbers.
Example:
0, 1, 2
But they can also be symbols or labels.
Example:
start
running
stopped
The key idea is separateness, not numerality.
Discrete values are about distinct options.
Discrete In Computation
Computation often works with discrete values.
Examples:
- bits
- symbols
- tokens
- states
- list positions
- graph nodes
These can be distinguished and manipulated step by step.
Discrete structure supports exact symbolic processing.
Discrete vs Continuous
Discrete values are separated.
Continuous values can vary through intermediate values.
Example:
discrete: number of files
continuous: file download progress
One counts separate objects.
The other can move through many intermediate percentages.
Discrete values jump between valid possibilities.
Final Summary
- Discrete values are separate and countable.
- They can be numbers, symbols, labels, or states.
- Discrete values have gaps between valid possibilities.
- Computation often uses discrete values.
- Discrete values contrast with continuous values.
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Continue the series.
Continuous Values