Paradoxes and Ambiguities
Paradoxes, ambiguities, and other uncertainties can offer playgrounds through which learners, explorers, enthusiasts can develop appreciation of the aesthetic, structural, and generative elements in mathematics. "Playing" with ambiguities in language, notation, context, or perception can invite the development of new ideas and knowledge, as well as foster skills in mathematical argumentation. Above all, playing in the realm of mathematics is just like playing anywhere else -- imaginative, creative, and just plain good fun.
This research focuses on the nuances of reasoning about, and with, mathematical infinities, paradoxes, and other ambiguities. At its core, this research is an exploration of techniques and abilities to cope cognitively with abstract mathematics. It seeks to offer a refined understanding of the tacit ideas and philosophies which can influence individuals' understanding infinity and resolution of ambiguities and paradoxical situations.
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