It was actually pretty constructive. I was trying to establish the existence of an equilibrium in a multi-period game with imperfect information. As the old map says: “Here be Dragons”. I left academia shortly thereafter…Was the fixed point algorithm constructive?I did see that in my feed today, and while it wasn’t necessarily the first time I’ve come across the idea, it so beats the combing a hairy billiard ball analogy (or aphorism, or whatever). I did once use a fixed point theorem in a paper, so it’s not a foreign idea to me (unless you count Polish, Dutch and Japanese as foreign).
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- Cuchulainn
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I mean, can it be programmed like Banach x_n = f(x_(n-1)) ..It was actually pretty constructive. I was trying to establish the existence of an equilibrium in a multi-period game with imperfect information. As the old map says: “Here be Dragons”. I left academia shortly thereafter…Was the fixed point algorithm constructive?I did see that in my feed today, and while it wasn’t necessarily the first time I’ve come across the idea, it so beats the combing a hairy billiard ball analogy (or aphorism, or whatever). I did once use a fixed point theorem in a paper, so it’s not a foreign idea to me (unless you count Polish, Dutch and Japanese as foreign).
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Yes, so solving for a special case would be straightforward. But, as discussed elsewhere, proof by example (or lack of counterexample) only gets you so far.
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- katastrofa
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Yeah, Banach is constructive. It gives a procedure which guarantees finding the (unique) fixed point. The thing is the task is not about metric spaces but about sets R2. So it has nothing to do with Banach. It’s bouwer’s fixed point theorem. This one isn’t constructive. It just says that *at least* one fixed point exists - if the set is convex and complete (hardly any country area). No clues how to find it.
I know the Internet ruled that it’s Banach but it’s wrong.
I know the Internet ruled that it’s Banach but it’s wrong.
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- Cuchulainn
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Things didn't wok well in the end for Brouwer.
He was related to our own @zeta.
BTW Sobolev spaces are the next level.
He was related to our own @zeta.
BTW Sobolev spaces are the next level.
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- katastrofa
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“ the model debunks huge numbers of stochastic SIR models in which the modellers just make up any old noise” — a random poet
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- katastrofa
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“ the model debunks huge numbers of stochastic SIR models in which the modellers just make up any old noise” — a random poet
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- katastrofa
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“The United States, a permanent member of the United Nations Security Council, has committed a grave violation of the UN Charter, international law and the NPT by attacking Iran's peaceful nuclear installations.”
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If I had $1 each time ChatGPT tells me it is the "final version" of the code he wrote down (tags, July 2024)