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Irrational Inquiries | A continuous injection of pure mathematicsA continuous injection of pure mathematics
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A continuous injection of pure mathematics
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About | Irrational Inquiries
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A continuous injection of pure mathematics. This is pretty much an expository math blog. As a Ph.D. student in pure mathematics, I’ve learned a lot over the past several years, and I enjoy explaining it to others. But this is often hard to do in conversation—usually the question is something like “What are you working on? I don’t intend to include any sort of original work on here, and probably not even anything cutting-edge. This blog is intended for serious lay people: I might assume some und...Address...
March | 2011 | Irrational Inquiries
https://polytopal.wordpress.com/2011/03
A continuous injection of pure mathematics. Monthly Archives: March 2011. The first infinite number. Wow, that was a much longer hiatus than I had planned. Let’s see if I can pick this up again. Last year, I spent several weeks describing in intricate detail what natural numbers are. If I had to describe my thesis in a sentence, this might be it:. 8220;The natural numbers are a computational tool for answering questions about finite sets.”. Here’s a somewhat longer and possibly more helpful recap. An obv...
Irrational Inquiries | A continuous injection of pure mathematics | Page 2
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A continuous injection of pure mathematics. Newer posts →. When the natural numbers are introduced from first principles, there’s a sort of standard narrative given for how addition, multiplication, and exponentiation work. Some of my mathier readers will probably recognize it instantly when I present it. In my considered opinion, this narrative is bullshit. Continue reading →. Click to email (Opens in new window). Click to share on Reddit (Opens in new window). Share on Facebook (Opens in new window).
Commutativity and all that | Irrational Inquiries
https://polytopal.wordpress.com/2010/10/20/commutativity-and-all-that
A continuous injection of pure mathematics. Equations, and undoing operations →. Commutativity and all that. One of the nice things about our new definitions. Of addition and multiplication is that they make proving basic properties of the operations a snap. Looking at the recursive definitions. It’s not at all obvious that 3 5 is 5 3, or that 4 5 is 5 4. Or, more accurately, it’s obvious for any. Are always equal. It happens that it is. Using a technique called induction. Might try to tell you that the.
Putting sets together | Irrational Inquiries
https://polytopal.wordpress.com/2010/10/18/putting-sets-together
A continuous injection of pure mathematics. Link love: The Unapologetic Mathematician. Commutativity and all that →. The goal of our program here is to understand arithmetic as an operation that “has something we do with sets.” This means that before we go further, I’ve got to explain the structure of sets a little more. I’ve got to be honest here: part of the reason it took me so long to write this post is because making basic set theory interesting is. Describe it very precisely. The union of “al...
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Irrational Inquiries | A continuous injection of pure mathematics
A continuous injection of pure mathematics. The first infinite number. Wow, that was a much longer hiatus than I had planned. Let’s see if I can pick this up again. Last year, I spent several weeks describing in intricate detail what natural numbers are. If I had to describe my thesis in a sentence, this might be it:. 8220;The natural numbers are a computational tool for answering questions about finite sets.”. Here’s a somewhat longer and possibly more helpful recap. Or “the same size”. An obvious next ...
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