This paper initiates a teaching sequence that focuses on building up equivalent definitions to the standard ones for the limit concept in Real Analysis. It comprises two parts: The first provides a classroom assignment where students, guided by Analysis lecturers, are led to develop an alternative definition to the [epsilon] - [delta] one for limits of one-variable real functions that are based on the realisation of the interval of [delta]'s. In the second one, students are directed by their instructor to restore equivalence between two distinct definitions of limit for a function mapping a subset of R[superscript 2] into R. This is done by adding a condition to one of the definitions, resulting in a third definition that "is" equivalent to the other one.