Timeline for Binary operation approximating "addition" on $2^\omega$
Current License: CC BY-SA 4.0
9 events
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| Jan 27, 2022 at 9:23 | history | edited | Dominic van der Zypen | CC BY-SA 4.0 |
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| Jan 26, 2022 at 22:32 | history | edited | Dominic van der Zypen | CC BY-SA 4.0 |
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| Jan 26, 2022 at 22:25 | comment | added | Dominic van der Zypen | I am still getting a grip on this simple but somehow weird operation. For me, it is the first example of a "non-associative group". No intuition as to the answer... | |
| Jan 26, 2022 at 21:10 | comment | added | LSpice | Oh, I see. @SamuelNeves's description of your option as "parallel carry propagation" helped me considerably to understand what was going on. Interesting question! Do you have any intuition for whether the answer should be 'yes' or 'no'? | |
| Jan 26, 2022 at 20:49 | history | edited | Dominic van der Zypen | CC BY-SA 4.0 |
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| Jan 26, 2022 at 20:43 | history | edited | Dominic van der Zypen | CC BY-SA 4.0 |
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| Jan 26, 2022 at 20:40 | comment | added | Dominic van der Zypen | Thanks for your question! One example for non-associativity is the following: Let $a: \omega \to 2$ be the function defined by $a(0) = 1$ and $a(n) = 0$ for $n \geq 1$. Let $b = a$, and let $c$ be defined by $c(0) = 0, c(1) = 1$ and $c(n) = 0$ for $n \geq 2$.. Then $a +' ( b +' c)$ is the constant $0$-function, whereas $(a +' (b+'c))(2) = 1$. For more examples, run the ${\tt C}$ program at github.com/dominiczypen/plus_approximation/blob/main/… | |
| Jan 26, 2022 at 16:39 | comment | added | LSpice | Could you mention an easy example of non-associativity? | |
| Jan 26, 2022 at 13:11 | history | asked | Dominic van der Zypen | CC BY-SA 4.0 |