What is the definition of magnitude?
Q: What is the definition of magnitude?
A: Magnitude is a property by which an object can be larger or smaller than other objects of the same kind. It is an ordering of the class of objects to which it belongs.
Q: What types of magnitudes did the Ancient Greeks distinguish between?
A: The Ancient Greeks distinguished between positive fractions, line segments (ordered by length), plane figures (ordered by area), solids (ordered by volume) and angles (ordered by angular magnitude).
Q: Did they consider negative magnitudes to be meaningful?
A: No, they did not consider negative magnitudes to be meaningful.
Q: How do we still primarily use magnitude today?
A: We still primarily use magnitude in contexts in which zero is either the lowest size, or less than all possible sizes.
Q: Did the Ancient Greeks prove that two types of magnitudes could not be the same?
A: Yes, they had proven that two types of magnitudes could not be the same, or even isomorphic systems of magnitude.
Q: What did they not consider when discussing different types of magnitudes?
A: They did not consider negative magnitudes to be meaningful when discussing different types of magnitudes.
Q:What was one way that Ancient Greeks ordered their different types of magnitudes?
A:The Ancient Greeks ordered their different types of magnitudes such as fractions, line segments, plane figures, solids and angles based on size - for example line segments were ordered by length and plane figures were ordered by area.
