Two different definitions of a Fuzzy number may be found in the literature. Both fulfill Goguen's Fuzzification Principle but are different in nature because of their different starting points. The first one was introduced by Zadeh and has well suited arithmetic and algebraic properties. The second one, introduced by Gantner, Steinlage and Warren, is a good and formal representation of the concept from a topological point of view. The objective of this paper is to analyze these definitions and discuss their main features.