Timeline for Why is 0 false?
Current License: CC BY-SA 3.0
13 events
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| Mar 24, 2018 at 0:13 | comment | added | Rémi Peyre | @supercat: On the other hand, one could argue that the main reason why XNOR is not regarded as fundamental is because it corresponds to the notion of coincidence, which can already be rendered as ‘==’. And equality /is/ undoubtedly a fundamental operator… | |
| May 9, 2017 at 17:10 | comment | added | supercat | @TonioElGringo: The difference between true and false is the difference between XOR and XNOR. One can form isomorphic rings using AND/XOR, where true is the multiplicative identity and false the additive one, or with OR and XNOR, where false is the multiplicative identity and true is the additive one, but XNOR is not usually regarded as a common fundamental operation the way XOR is. | |
| Nov 17, 2015 at 16:08 | comment | added | TonioElGringo |
This answer doesn't make sense. true is also the identity and the zero of semirings (Boolean and/or). There is no reason, appart convention, to consider false is closer to 0 than true.
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| Nov 12, 2013 at 19:38 | history | edited | Jon Purdy | CC BY-SA 3.0 |
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| Oct 5, 2013 at 3:48 | comment | added | Andyz Smith | I'm unclear whether the fact that they are isomorphic algebras is being proved or used as an assumption here. | |
| Sep 5, 2013 at 4:16 | history | edited | Jon Purdy | CC BY-SA 3.0 |
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| Sep 5, 2013 at 4:04 | history | edited | Jon Purdy | CC BY-SA 3.0 |
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| Sep 5, 2013 at 3:09 | comment | added | Siyuan Ren | Boolean OR has no inverse. How does that form a ring? | |
| May 22, 2013 at 9:37 | vote | accept | Morwenn | ||
| May 16, 2013 at 15:22 | comment | added | Jimmy Hoffa | +1 for giving details of a concrete and very old maths in which this has been followed and long made sense | |
| May 16, 2013 at 9:20 | comment | added | l0b0 | +1 for referring to similar identities. Finally an answer which doesn't just boil down to "convention, deal with it". | |
| May 16, 2013 at 7:58 | comment | added | Giorgio |
Nice that you mentioned lists. (BTW, nil is both the empty list [] and the false value in Common Lisp; is there a tendency to merge identities from different data types?) You still have to explain why it is natural to consider false as an additive identity and true as a multiplicative identity and not the other way around. Isn't possible to consider true as the identify for AND and zero for OR?
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| May 16, 2013 at 3:47 | history | answered | Jon Purdy | CC BY-SA 3.0 |