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| Axioms; Split from "Difference between 'knowledge' and 'belief'? | |
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| Tweet Topic Started: Jan 1 2011, 04:42 PM (517 Views) | |
| CJ | Jan 1 2011, 04:42 PM Post #1 |
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A very minor case of serious brain damage
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Interesting way to look at it. Now, another question. We can't get very far at all if we have to rely solely on things we can prove 100%; in order to get anywhere, we need to assume certain things that are taken to be self-evident. (We even have to do this in mathematics: before rigorously proving anything, we have to assume a set of axioms). Two assumptions that I make are that the universe exists, and that we can learn about it. How would these assumptions be classified under this system? (Or would they be something else entirely?) Of course, now we're out of science and into philosophy, which, as you can probably tell, is a subject I'm substantially less well-informed about .
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Jan 2 2011, 01:50 AM Post #2 |
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I'm pretty good at philosophy, but everything I know about it is self-taught. But your talk of science and mathematics has lost me here. I don't believe I know of axioms, or a system of axioms, and I am lost as to what you count as "self-evident." |
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| CJ | Jan 2 2011, 01:55 AM Post #3 |
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Oh, OK. An 'axiom' is one of those assumptions that's taken as self-evident and therefore not requiring any proof. Here are some examples of 'axioms' from mathematics: 1) For any real numbers a and b, a + b = b + a; 2) For any real number a, a + 0 = a, and 1a = a. Once we assume a few simple and obvious things like that, we can use them to start proving harder stuff. |
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Jan 2 2011, 07:16 PM Post #4 |
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Oh, I see! Those are like properties (additive and communicative). Edited by thecostumedanceparty, Jan 2 2011, 07:17 PM.
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| CJ | Jan 2 2011, 07:26 PM Post #5 |
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Yeah, that's basically what they are. We also have to assume that 0 is not equal to 1 (since if it was, all numbers would be equal to 0, which would be very dull and not very useful at all). |
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| Michelle | Jan 2 2011, 07:37 PM Post #6 |
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I thought sometimes it is equal to 1?
Edited by Michelle, Jan 2 2011, 07:37 PM.
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| CJ | Jan 2 2011, 09:33 PM Post #7 |
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I don't think so. Sometimes 0 is equal to 2, or 3, but I've never heard of it being equal to 1. |
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| Michelle | Jan 2 2011, 09:37 PM Post #8 |
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In n factorial you said it did... |
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| CJ | Jan 2 2011, 09:44 PM Post #9 |
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Oh, that's something different. 0! (0 factorial) = 1, but that doesn't mean 0 = 1. |
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| Michelle | Jan 3 2011, 01:18 AM Post #10 |
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Oh, all right. I got confused. That's what I was talking about.
Edited by Michelle, Jan 3 2011, 01:29 AM.
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Jan 4 2011, 01:25 PM Post #11 |
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I don't understand how you can say 0 = 2. They are completely different numbers with a plethora of possibilities in-between them. |
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| Michelle | Jan 4 2011, 04:04 PM Post #12 |
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I think someone needs to learn about modular arithmetic. ![]() I can't teach it myself, but I can give an example, thanks to CJ <3 77 modulo 8 = 9 remainder 5 77 = 5 (modulo 8) Basically, you divide 77 into 8 and you get 9 remainder 5 hence why 77 = 5 (modulo 8) 126 modulo 8 = 15 remainder 6 126 = 6 (modulo 8) I'm not sure why 0 = 2, CJ enlighten me please (Unless I figure it out myself...) Edited by Michelle, Jan 4 2011, 04:08 PM.
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| CJ | Jan 4 2011, 10:49 PM Post #13 |
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Modular arithmetic is a form of arithmetic which 'wraps around' when you get up to a certain number. It's also known as 'clock arithmetic', mainly because clocks are a good example of an everyday application. You go from 1 o'clock to 2 o'clock, then 3 o'clock, and so on up to 12 o'clock. After that, though, you don't go to 13 o'clock: you go back to 1 o'clock. Because "13 o'clock" would basically be the same thing as 1 o'clock, this is an example of a system in which 13 = 1; subtract one from both sides, and you get 12 = 0. However, if your clock only had 2 numbers (instead of 12), then you'd only have 1 o'clock and 2 o'clock. 3 o'clock would basically be the same thing as 1 o'clock, so you would have constructed a system in which 3 = 1 (and hence, 2 = 0). (Also, in this type of 'modular arithmetic', we usually only bother with the integers, and not any of the fractions and decimals in between. We don't consider things like 'half past two' - which, to be honest, I think is a bit odd). Of course, in the 'usual' arithmetic that we're all used to, 0 and 2 are indeed, as you say, completely different numbers with a plethora of possibilities in-between them. That's not the only form of arithmetic there is, though: modular arithmetic is an example of another type. |
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| Michelle | Jan 4 2011, 11:13 PM Post #14 |
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Aww I wish I could have known that before! Oh well, I hadn't thought of it like that. Interesting. |
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| CJ | Jan 5 2011, 02:16 PM Post #15 |
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Sorry I forgot to mention clocks before....it's such an obvious example, I can't believe I missed it >_< . |
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| Michelle | Jan 5 2011, 03:48 PM Post #16 |
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Oh, don't worry. You can reteach me that if you want to. |
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8:35 AM Jul 11