RUME 25
2023
Omaha, Nebraska
How Do We Disentangle Equality from Equivalence? Well, It Depends
Page: 315
In this paper, we report on interviews with mathematicians exploring the ways in which they think about the relationship between equality and equivalence. Given sometimes unclear and conflicting presentations of equality and equivalence in the literature, we are motivated to understand subtleties about how these constructs interact; doing so can have pedagogical implications, which we explore in this paper. We present three major themes that emerged from our analysis of the mathematicians’ discussions of equality: 1) that equality represents a well-specified equivalence relation, 2) that audience matters when specifying equivalence and equality, and 3) that context is imperative when discussing equivalence and equality.