How to read a definition
In Geometry . . . men begin at settling the significations of their words; which . . . they call Definitions.
Thomas Hobbes, Leviathan, 1651
Precise definitions are vital in high-level mathematics. We need precision so that we can all agree on what we are talking about. Nonetheless, owing to personal preferences, definitions may vary slightly from mathematician to mathematician so it pays to be vigilant.
The reason for giving a mathematical object a particular name is often lost in the mists of time. Frequently ...