The way we avoid ambiguities in mathematics is to provide concrete and rigorous definitions. Crafting good definitions is not easy, but it is incredibly important. The definition is the agreed upon st...The way we avoid ambiguities in mathematics is to provide concrete and rigorous definitions. Crafting good definitions is not easy, but it is incredibly important. The definition is the agreed upon starting point from which all truths in mathematics proceed. Is there a graph with no edges? We have to look at the definition to see if this is possible. We want our definition to be precise and unambiguous, but it also must agree with our intuition for the objects we are studying.
