This is my dynamic home page. It is very experimental, in the sense that I’m not sure what I’m going to write about or what feedback I am seeking. I expect I’ll focus on set theory, since that is my primary research area. But I hope to also touch on logic, general mathematics, math learning, and math on the web. Let’s see how it goes!
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I am currently a postdoc at York University and the Fields Institute in Toronto. Check out my vitae page to learn more about me!
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Chatter- Comment on My favorite proof that $\mathbb R$ is uncountable by Zach TeitlerMatt, a decreasing sequence of intervals in the real numbers always has a nonempty intersection (a point in the intersection of all the intervals), but a decreasing sequence of intervals in the rationals may have an empty intersection. Consider, say, the intervals [a_n, b_n] where a_1 = 1, b_1 = 2, b_{n+1} = (a_n+b_n)/2, and a_{n+1} = 2/b_{n+1}. Then the end […]Zach Teitler
- Comment on My favorite proof that $\mathbb R$ is uncountable by Joel David HamkinsSam, although sometimes people make a big fuss about this proof being different from the diagonalization proof using digits, I don't see them as truly different. After all, fixing an initial segment of the digits of a real amounts to fixing a certain interval, the interval of reals whose digits begin that way. And so choosing the digits to avoid a certa […]Joel David Hamkins
- Comment on My favorite proof that $\mathbb R$ is uncountable by Samuel CoskeyIn the argument we construct a decreasing sequence of intervals $[a_n,b_n]$. We then argue that there must be a point $x$ in the intersection of all these intervals---but we never argued that $x$ is rational! So this wouldn't give any contradiction if you confined yourself to just the rational numbers. […]Samuel Coskey
- Comment on My favorite proof that $\mathbb R$ is uncountable by MattI understand why the proof works, but what is to stop us from using the same argument on the rational numbers? Because they are dense, couldn't we always choose an interval that excludes the most recent element in the sequence? Where is the contradiction? […]Matt
- Comment on Special uncountable trees by safThe above is a proof of the c.c.c. property for a poset which is not Knaster, and indeed the reasoning is different than the ``$\Delta$-system plus refinements'' method. [btw, while the ultrafilter argument is very elegant, one can still do without it]. Note that if a poset is not Knaster, then a ``$\Delta$-system plus refinements'' argum […]saf
- Comment on My favorite proof that $\mathbb R$ is uncountable by Zach Teitler
Booles' Rings
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