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| | xorshammer.com
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| | 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...
| | unstableontology.com
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| | (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...
| | jeremykun.wordpress.com
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| | We assume the reader is familiar with the concepts of determinism and finite automata, or has read the corresponding primer on this blog. The Mother of All Computers Last time we saw some models for computation, and saw in turn how limited they were. Now, we open Pandrora's hard drive: Definition: A Turing machineis a...
| | boldandgreen.wordpress.com
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| I tried a new background color for my windows as shown here. Instead of the light grey suggested, I picked a very light brown: R 230 Y 222 B 188 (as shown on picture). The best thing is to change the background in Word first and test the color.