Mathematics

Steve Patterson, among many points of objection, is doubtful on the modern concept of infinity (or more strictly the transfinite): The foundations of modern mathematics are flawed. A logical contradiction is nestled at the very core, and it’s been there for a century. Of all the controversial ideas I hold, this is the most radical. I disagree with nearly all professional mathematicians, and I think they’ve made an elementary error that most children would discover. It’s about infinity. I’ve written about infinity here, here, and here, and each article points to the same conclusion: There are no infinite sets. Not only do infinite sets not exist, but the very concept is logically contradictory – no different than “square circles”. Infinite Read More ›

Over at YouTube, there is a bit of history of Math, on study of cubic functions — and yes there is as usual, some less than exemplary detail — that led to the “invention” of imaginary numbers: Now of course, I contend that this was discovery not invention (I often don’t buy Veritas Sum’s narrative, but here is a way to see the story). In News’ thread on i, I commented at 33: your definition [– Eugene at 8: “there exists such a pair of real numbers (0, 1) that (0, 1) * (0, 1) = -1, where “*” is the specific multiplication rule defined for these types of pairs” –] is tantamount to describing the role of sqrt – Read More ›