Explore >> Select a destination
|
You are here 
|
daniellefong.com | ||
| | | | |
unstableontology.com
|
|
| | | | | (note: one may find the embedded LaTeX more readable on LessWrong) The Löwenheim-Skolem theorem implies, among other things, that any first-order theory whose symbols are countable, and which has an infinite model, has a countably infinite model. This means that, in attempting to refer to uncountably infinite structures (such as in set theory), one "may... | |
| | | | |
dvt.name
|
|
| | | | | In the previous blog post in this series, we looked at Gödel's First Incompleteness Theorem, and came to the amazing conclusion that we can't compute certain kinds of functions in formal systems (like Javascript). Specifically, we looked at a special function, , which turned out to be non-computable. In case we forgot, the first incompleteness ... | |
| | | | |
xorshammer.com
|
|
| | | | | There are many functions from $latex \mathbb{N}$ to $latex \mathbb{N}$ that cannot be computed by any algorithm or computer program. For example, a famous one is the halting problem, defined by $latex f(n) = 0$ if the $latex n$th Turing machine halts and $latex f(n) = 1$ if the $latex n$th Turing machine does not... | |
| | | | |
scottaaronson.blog
|
|
| | | Way back in 2005, I posed Ten Semi-Grand Challenges for Quantum Computing Theory, on at least half of which I'd say there's been dramatic progress in the 16 years since (most of the challenges were open-ended, so that it's unclear when to count them as "solved"). I posed more open quantum complexity problems in 2010,... | ||
