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Inductive proofs are one of the first types of formal theorem proving students run across. There is good reason for this; it’s easy to teach and powerful (and comes in handy for the piles of complexity analyses I’ve assigned my students this week).
As a quick refresher, in an induction proof you are trying to show that f(n)=g(n) by first showing that f(0)=g(0), and then assuming that f(k)=g(k) for some k<n. If you can show that, given these results, f(k+1)=g(k+1), you’ve shown that f(n)=g(n). QED.
This is about where you should be suspicious. We picked k arbitrarily, right? This is about where people tell you that you have some “well-ordered” numbers.
The hardest part of starting a blog is trying to decide what piece of your life is worth sharing given the limited and valuable attention of the people you want reading it.
This blog will be a weekly-ish rundown of a technical topic I found interesting, likely from my teaching or research. I will post other essay drafts or position papers as time permits. As for why; I miss reading long-form blogs. I miss LJ. I miss discussions that weren’t maybe always professional but were thoughtful and engaged. Doing interdisciplinary work often involves filling everyone you talk to in on so much background that you don’t get to the meat of your problems. It is too easy to veer off into an area that, in my case, I likely know as little about as the person I’m talking to, but my credentials mean I need to at least postulate.
Don’t worry, I tell them I don’t know. That doesn’t seem to stop people though?
In any case, I promise to tell you when I don’t know what I’m talking about, and as a scientist I shouldn’t need to say this, but criticism is what turns my world.
Be seeing you.
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