Monthly Archives: October 2024

ChatGPT

Posted on October 18, 2024 by Persiflage

I gave ChatGPT the midterm. It scored around 60/100. (Update: I just graded the midterm and was more generous, so 65/100.) It failed miserably on the graphing question, which is maybe expected since it doesn’t have the ability scan in … Continue reading →

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The game of infinite intelligence

Posted on October 12, 2024 by Persiflage

I’ve talked about how analyzing games naturally leads to inductive arguments, and gave a few examples. Here is a tricky game problem which is a little mind bending. It’s much tricker than anything else I have suggested, so consider it … Continue reading →

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The Sticks Game

Posted on October 9, 2024 by Persiflage

Although I did this in class, I thought it might be useful to write out a proof here. There are many variations, but it should look something quite similar to this. Claim: For \(n = 0,1,2,\ldots\) a non-negative integer, the … Continue reading →

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Constructing Irrational Numbers using Cantor’s Argument

Posted on October 4, 2024 by Persiflage

Cantor’s argument also allows us to “explicitly” construct irrational numbers. Let’s take a list which includes all the rational numbers between \(0\) and \(1\). First we add \(1\), and then we take \(a/b\) first over the possible denominators \(b > … Continue reading →

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