Magnitude (mathematics)

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.

In mathematical language one would say: It is an ordering of the class of objects to which it belongs.

The Ancient Greeks distinguished between several types of magnitude, including:

• (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.