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What is an independent variable?

What is an independent variable? Here are some definitions.

Noun
  1. (algebra) In an equation, any variable whose value is not dependent on any other in the equation.
  2. (sciences) The variable that is changed or manipulated in a series of experiments.
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Examples
In a global economy, ecology can no longer be taken as an independent variable, as economists are wont to do.
Evaluate the indefinite integral with the independent variable set to each of the limits.
If a function calls another function, then resolves all references to other functions in terms of their independent variable.
This is the name of the preferred independent variable for algebraic and calculus applications.
In other words, it was more interested in the concept as an independent variable used to explain other social phenomena.
In fact, not one of the four studies looked at education coursework as an independent variable.

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