Does it matter how you define the error in a numerical solution?

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The discussion centers on the importance of defining error in numerical solutions, specifically contrasting the numerical solution with the exact solution. It emphasizes that while the magnitude of error is crucial, the sign serves primarily for clarity. The conventional representation of error is presented as V ± E, where V denotes the value and E represents the error. Understanding this distinction is essential for accurate reporting and interpretation of numerical results.

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Does it matter how you define the error in a numerical solution??

If you define the error as numerical solution - exact solution would you be hugely wrong even if you understood what was happening (i know it's the negative of exact - numerical). I wrote a report at uni and realized i defined the error in this way
 
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Usually when talking about error, the magnitude is most important. The sign is only for clarity.

Typical presentation is V ± E, where V is the value and E is the error.
 
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