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Numbers, Algebra, Discrete vs Continuous
Continuous Values
Continuous values can vary through intermediate values rather than jumping between separate options.
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Continuous Values
Definition
Continuous values can vary through intermediate values.
Example:
2.0
2.1
2.01
2.001
Between two continuous values, more values can exist.
Continuous value = value that can vary smoothly within a range.
Simple Examples
Continuous quantities often come from measurement.
Examples:
height
weight
distance
temperature
time
position
A distance might be:
2 meters
2.5 meters
2.57 meters
Continuous values support fine-grained measurement.
Continuous vs Discrete
Discrete:
number of nodes = 4
Continuous:
distance = 4.37 meters
You usually cannot have 4.37 nodes.
But you can measure 4.37 meters.
Discrete counts separate units; continuous measures variable quantities.
Real Numbers And Continuity
Real numbers are used to model continuous values.
Example:
position on a line
The position can be:
0
0.5
0.51
0.511
The model allows increasingly precise positions.
Real numbers give a mathematical language for continuity.
Computation And Approximation
Computers usually store continuous values approximately.
Example:
temperature = 21.438
The stored value has limited precision.
The real-world quantity may vary more finely than the stored representation.
Continuous quantities often become finite approximations inside computation.
Final Summary
- Continuous values can vary through intermediate values.
- They are common in measurement.
- Real numbers model continuous values.
- Discrete values count separate options.
- Computers usually approximate continuous values with finite representations.
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Continue the series.
Algebraic Expression