The magnitude of a mathematical object is its size: a property by which it can be larger or smaller than other objects of the same kind.
- (positive) fractions
- line segments (ordered by length)
- Plane figures (ordered by area)
- Solids (ordered by volume)
- Angles (ordered by angular magnitude)
They had proven that the first two could not be the same, or even isomorphic systems of magnitude. They did not consider negative magnitudes to be meaningful, and magnitude is still primarily used in contexts in which zero is either the lowest size, or less than all possible sizes.
- | x | = x, if x ≥ 0
- | x | = -x, if x < 0
This gives the number's distance from zero on the real number line. For example, the modulus of -5 is 5.
A magnitude is never negative. When comparing magnitudes, it is often helpful to use a logarithmic scale. Real-world examples include the loudness of a sound (decibel), the brightness of a star, or the Richter scale of earthquake intensity.
Because magnitudes are often not linear, they usually cannot be added or subtract in a meaningful way.
- "Comprehensive List of Algebra Symbols". Math Vault. 2020-03-25. Retrieved 2020-08-23.
- "Magnitude Definition (Illustrated Mathematics Dictionary)". www.mathsisfun.com. Retrieved 2020-08-23.
- Nykamp, Duane. "Magnitude of a vector definition". Math Insight. Retrieved August 23, 2020.