Welcome Guest [Log In] [Register]

This board is closed and will be kept as an archive. Please head to our new home at tch-forum.com



(Existing members: Please check your PMs for your password on the new board. If you do not have a PM, then please send one to me)



Welcome to The Coffee House - your dose of caffeine!

The Coffee House is a friendly and informal community dedicated to having fun. We're a diverse bunch, and so we have plenty to offer, including:
  • Discussions on a wide range of subjects, from science and current events to sport and gaming (and most things in between!);
  • Community-centered forums where members can get to know each other better, and share things they've made;
  • Regularly-scheduled contests, where members can compete for awards and forum currency (Coffee Credits);
  • Shops, where members may spend the Coffee Credits they've earned;
  • A Discord server, where anyone can chat to our members in real time.
What you can see below is a snapshot of what we have to offer. To see the rest, and gain access to all of this, all you need to do is register as a member. Registration is quick, free and easy.

Join our community!

If you're already a member please log in to your account to access all of our features:

Username:   Password:
Add Reply
Axioms; Split from "Difference between 'knowledge' and 'belief'?
Topic Started: Jan 1 2011, 04:42 PM (517 Views)
CJ
Member Avatar
A very minor case of serious brain damage

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 :P .
Offline Profile Quote Post Goto Top
 
thecostumedanceparty
Member Avatar


KingsIndian
Jan 1 2011, 04:42 PM
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 :P .
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."
Offline Profile Quote Post Goto Top
 
CJ
Member Avatar
A very minor case of serious brain damage

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.
Offline Profile Quote Post Goto Top
 
thecostumedanceparty
Member Avatar


KingsIndian
Jan 2 2011, 01:55 AM
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.
Oh, I see! Those are like properties (additive and communicative).
Edited by thecostumedanceparty, Jan 2 2011, 07:17 PM.
Offline Profile Quote Post Goto Top
 
CJ
Member Avatar
A very minor case of serious brain damage

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).
Offline Profile Quote Post Goto Top
 
Michelle
No Avatar
.

I thought sometimes it is equal to 1?
Edited by Michelle, Jan 2 2011, 07:37 PM.
Offline Profile Quote Post Goto Top
 
CJ
Member Avatar
A very minor case of serious brain damage

I don't think so. Sometimes 0 is equal to 2, or 3, but I've never heard of it being equal to 1.
Offline Profile Quote Post Goto Top
 
Michelle
No Avatar
.

In n factorial you said it did...
Offline Profile Quote Post Goto Top
 
CJ
Member Avatar
A very minor case of serious brain damage

Oh, that's something different. 0! (0 factorial) = 1, but that doesn't mean 0 = 1.
Offline Profile Quote Post Goto Top
 
Michelle
No Avatar
.

Oh, all right. I got confused. That's what I was talking about.
Edited by Michelle, Jan 3 2011, 01:29 AM.
Offline Profile Quote Post Goto Top
 
thecostumedanceparty
Member Avatar


I don't understand how you can say 0 = 2. They are completely different numbers with a plethora of possibilities in-between them.
Offline Profile Quote Post Goto Top
 
Michelle
No Avatar
.

I think someone needs to learn about modular arithmetic. :P

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.
Offline Profile Quote Post Goto Top
 
CJ
Member Avatar
A very minor case of serious brain damage

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.
Offline Profile Quote Post Goto Top
 
Michelle
No Avatar
.

Aww I wish I could have known that before! Oh well, I hadn't thought of it like that. Interesting.
Offline Profile Quote Post Goto Top
 
CJ
Member Avatar
A very minor case of serious brain damage

Sorry I forgot to mention clocks before....it's such an obvious example, I can't believe I missed it >_< .
Offline Profile Quote Post Goto Top
 
Michelle
No Avatar
.

Oh, don't worry. You can reteach me that if you want to.
Offline Profile Quote Post Goto Top
 
1 user reading this topic (1 Guest and 0 Anonymous)
« Previous Topic · Science and Nature · Next Topic »
Add Reply


Anti-Spam Bots! Mazeguy Smilies