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Category: Set Theory

A Note on Russell’s Paradox

A Note on Russell’s Paradox

Topics in mathematics very frequently rely on set theory (I am hard-pressed to quickly think of one that doesn't). Set theory itself is a very abstract area of study. Even so, mathematicians built it on axioms (self-evident truths taken as fundamental starting points), and, of course, debate continues to this day as to which axioms…

Concatenation as an Operation

Concatenation as an Operation

Mathematics is like any activity, sport, or skill: it must be honed and practiced. With that in mind, I have been bolstering up my abilities in algebra with a fantastic book A Book of Abstract Algebra, by Charles C. Pinter.. As I go through the chapters, I will be posting and discussing selected relevant exercises that…

The Rigor of Fuzzy Sets

The Rigor of Fuzzy Sets

Perhaps "fuzzy set theory", "fuzzy arithmetic", and "fuzzy rules" could have been named something a bit less mock-worthy. The word "fuzzy" has English synonyms "blurred", "unfocused", and the worst "ill-defined". However, fuzzy set theory is anything but fuzzy. Maybe cuddly and fun, but certainly not ill-defined. We'll take a look in this post at what…