##### FC-11 - Set Theory

Basic mathematical set theory is presented and illustrated with a few examples from GIS. The focus is on set theory first, with subsequent interpretation in some GIS contexts ranging from story maps to municipal planning to language use. The breadth of interpretation represents not only the foundational universality of set theory within the broad realm of GIS but is also reflective of set theory's fundamental role in mathematics and its numerous applications. Beyond the conventional, the reader is taken to see glimpses of set theory not commonly experienced in the world of GIS and asked to imagine where else they might apply. Initial broad exposure leaves room for the mind to grow into deep and rich fields flung far across the globe of academia. Direction toward such paths is offered within the text and in additional resources, all designed to broaden the horizons of the open-minded reader.

## FC-21 - Resolution

Resolution in the spatial domain refers to the size of the smallest measurement unit observed or recorded for an object, such as pixels in a remote sensing image or line segments used to record a curve. Resolution, also called the measurement scale, is considered one of the four major dimensions of scale, along with the operational scale, observational scale, and cartographic scale. Like the broader concept of scale, resolution is a fundamental consideration in GIScience because it affects the reliability of a study and contributes to the uncertainties of the findings and conclusions. While resolution effects may never be eliminated, techniques such as fractals could be used to reveal the multi-resolution property of a phenomenon and help guide the selection of resolution level for a study.