[2/25/2006 3:15 PM] <qwertydawom> k
[2/25/2006 3:15 PM] <qwertydawom> just one question though
[2/25/2006 3:16 PM] <qwertydawom> do you all know what Venn diagrams are?
[2/25/2006 3:16 PM] <Ch4r> yes
[2/25/2006 3:18 PM] <qwertydawom> others know it too?
[2/25/2006 3:19 PM] <Elmo_> yes
[2/25/2006 3:20 PM] <qwertydawom> alright, for those who don't answer and don't know what it is : http://www.sdcoe.k12.ca.us/score/actbank/tvenn.htm
[2/25/2006 3:20 PM] <qwertydawom> now, I can begin :)
[2/25/2006 3:21 PM] <qwertydawom> So, in our last lectures, we studied the 'union' and 'interesction' of sets.
[2/25/2006 3:21 PM] <qwertydawom> And, there are rules that apply to these operators.
[2/25/2006 3:22 PM] <qwertydawom> If you use Venn diagrams, it should be very easy to check these rules. :)
[2/25/2006 3:22 PM] <qwertydawom> There are three main properties :
[2/25/2006 3:22 PM] <qwertydawom> 1° Commutivity :
[2/25/2006 3:22 PM] <qwertydawom> A inter B = B inter A
[2/25/2006 3:22 PM] <qwertydawom> A U B = B U A
[2/25/2006 3:23 PM] <qwertydawom> is it ok? 
[2/25/2006 3:23 PM] <--| Syr0kill has left #lecture (Leaving)
[2/25/2006 3:24 PM] -->| grimR (grim@bu-486EF152.hsd1.md.comcast.net) has joined #lecture
[2/25/2006 3:24 PM] <Ch4r> yea..
[2/25/2006 3:24 PM] <qwertydawom> alright, so, 2nd property :
[2/25/2006 3:24 PM] <qwertydawom> 2° Associativity :
[2/25/2006 3:25 PM] <qwertydawom> (A inter B) inter C = A inter (B inter C)
[2/25/2006 3:25 PM] <qwertydawom> (A U B) U C = A U (B U C)
[2/25/2006 3:25 PM] <qwertydawom> ok?
[2/25/2006 3:25 PM] * Ch4r nods
[2/25/2006 3:25 PM] <Elmo_> yep
[2/25/2006 3:25 PM] <qwertydawom> k
[2/25/2006 3:26 PM] <qwertydawom> so, 3rd property :
[2/25/2006 3:26 PM] <qwertydawom> 3° Distributivity :
[2/25/2006 3:26 PM] <qwertydawom> A inter (B U C) = (A inter B) U (A inter C)
[2/25/2006 3:26 PM] <qwertydawom> A U (B inter C) = (A U B) inter (A U C)
[2/25/2006 3:27 PM] <qwertydawom> alright?
[2/25/2006 3:27 PM] <Ch4r> mhm
[2/25/2006 3:27 PM] <qwertydawom> you can see it if you use Venn diagrams ;)
[2/25/2006 3:28 PM] <qwertydawom> tell me when it's ok
[2/25/2006 3:29 PM] <Ch4r> it's ok :p
[2/25/2006 3:29 PM] <qwertydawom> ok ;)
[2/25/2006 3:29 PM] <Elmo_> there's another property. I forgot =|
[2/25/2006 3:30 PM] -->| Narada (Node1@bu-869AAE49.client.mchsi.com) has joined #lecture
[2/25/2006 3:30 PM] <Narada> Sorry I'm late.
[2/25/2006 3:30 PM] <Ch4r> np, just stfu and learn ;)
[2/25/2006 3:30 PM] <Narada> hehe
[2/25/2006 3:31 PM] <Elmo_> the long version of npjstfual
[2/25/2006 3:31 PM] <qwertydawom> ok, so, now we've seen those three rules
[2/25/2006 3:32 PM] <qwertydawom> who makes the connection with algebra and show me algebra operators for which these rules apply? :)
[2/25/2006 3:32 PM] <Elmo_> hrmmm
[2/25/2006 3:32 PM] <Elmo_> *looks on the calculator keys*
[2/25/2006 3:32 PM] <Ch4r> commutivity: a*b = b*a, right?
[2/25/2006 3:32 PM] <Elmo_> yep
[2/25/2006 3:33 PM] <Ch4r> w00t
[2/25/2006 3:33 PM] <Ch4r> ;P
[2/25/2006 3:33 PM] <Elmo_> distributive = a(bc) ab+ac
[2/25/2006 3:33 PM] <Elmo_> no
[2/25/2006 3:33 PM] <Elmo_> a(b+c) ab+ac
[2/25/2006 3:33 PM] <qwertydawom> yes :)
[2/25/2006 3:33 PM] <qwertydawom> and associative?
[2/25/2006 3:33 PM] <Ch4r> associativity: a*b*c = a*c*b
[2/25/2006 3:34 PM] <Elmo_> abc = acb = cab = bac 
[2/25/2006 3:35 PM] <qwertydawom> you need parentheses :)
[2/25/2006 3:35 PM] <qwertydawom> what you show here is just commutativity
[2/25/2006 3:35 PM] <Narada> a(bc)=b(ac)
[2/25/2006 3:36 PM] <qwertydawom> and.. Narada is... right! :)
[2/25/2006 3:36 PM] <qwertydawom> another one : a+(b+c) = (a+b)+c :)
[2/25/2006 3:37 PM] <qwertydawom> Ok, so now, you remember that we've seen the TRUTH tables, right?
[2/25/2006 3:37 PM] <Elmo_> maybe
[2/25/2006 3:37 PM] =-= Mode #lecture +m  by qwertydawom
[2/25/2006 3:37 PM] =-= Mode #lecture +v Ch4r by qwertydawom
[2/25/2006 3:37 PM] =-= Mode #lecture +v Elmo_ by qwertydawom
[2/25/2006 3:37 PM] =-= Mode #lecture +v Narada by qwertydawom
[2/25/2006 3:38 PM] <qwertydawom> So, we are now going to explain the meaning of 'truth' in mathematics.
[2/25/2006 3:38 PM] <qwertydawom> Definition : Something is said to be true if there are NO exceptions.
[2/25/2006 3:39 PM] <qwertydawom> In life, when we say something is true, we take it as 'most of the times it's true'.
[2/25/2006 3:40 PM] <qwertydawom> For example, when we say that Linux owns Windows, it doesn't mean that every single distro owns it, but just that most do! :)
[2/25/2006 3:40 PM] <qwertydawom> -sorry for having chosen this.. oh so controversial subject- :P
[2/25/2006 3:40 PM] * Ch4r glares
[2/25/2006 3:40 PM] <Ch4r> ;)
[2/25/2006 3:40 PM] <Elmo_> ./lecture -flame.war
[2/25/2006 3:40 PM] <Narada> I thought it was funny...
[2/25/2006 3:41 PM] <qwertydawom> :)
[2/25/2006 3:41 PM] <qwertydawom> But, for mathematicians, it isn't the same thing, if it's true, then there should be NO exceptions.
[2/25/2006 3:41 PM] <qwertydawom> Let's take an example.
[2/25/2006 3:42 PM] <Elmo_> like Suse or Ubuntu :-)
[2/25/2006 3:42 PM] <qwertydawom> The inverse (or 'reciprocal') of a number is : one divided by this number.
[2/25/2006 3:42 PM] <qwertydawom> e.g. : the inverse of 5 is : 1/5
[2/25/2006 3:42 PM] <qwertydawom> Now, is the following sentence true? :
[2/25/2006 3:43 PM] <qwertydawom> "Every number has an inverse"
[2/25/2006 3:43 PM] <Narada> Yes.
[2/25/2006 3:43 PM] <qwertydawom> You fell in the trap! :)
[2/25/2006 3:43 PM] <Ch4r> 0 ;x
[2/25/2006 3:43 PM] <Narada> fuck
[2/25/2006 3:43 PM] <Elmo_> tehee
[2/25/2006 3:43 PM] <Narada> It always works if you press 1/x on my calculator. :(
[2/25/2006 3:43 PM] <qwertydawom> Ch4r pointed out the flaw in your reasoning ;)
[2/25/2006 3:44 PM] <Narada> aw nuts
[2/25/2006 3:44 PM] <qwertydawom> For x = 0, 1/x isn't defined :)
[2/25/2006 3:44 PM] <qwertydawom> So, we can't say that the sentence is true.
[2/25/2006 3:44 PM] <Ch4r> *ahem*
[2/25/2006 3:44 PM] <Ch4r> d'you mean false?
[2/25/2006 3:44 PM] <Elmo_> *can't*
[2/25/2006 3:45 PM] <qwertydawom> That's right that it is true for most of the numbers, but since it isn't true for the number 0 (being the exception), our sentence is mathematically false. :)
[2/25/2006 3:45 PM] <Ch4r> Elmo_, whoops -_-
[2/25/2006 3:45 PM] <qwertydawom> And now, Narada, another one for you, tell me if this sentence is true :
[2/25/2006 3:46 PM] <Narada> oh goodie
[2/25/2006 3:46 PM] <qwertydawom> "Every natural number is either odd or even"
[2/25/2006 3:46 PM] <Elmo_> *cough*
[2/25/2006 3:46 PM] <Narada> No, 0 is a natural number isn't it?  err... I thought I remember it being called even before, but it is controversial, so I'm not sure. :/
[2/25/2006 3:47 PM] <Narada> Natural numbers are 0 and up correct?
[2/25/2006 3:47 PM] <qwertydawom> Yes ;)
[2/25/2006 3:47 PM] <qwertydawom> So? True or false?
[2/25/2006 3:47 PM] <Narada> Well if 0 is even, it's true; if 0 is neutral, it's false. :p
[2/25/2006 3:48 PM] <qwertydawom> 0 is even :)
[2/25/2006 3:48 PM] <Elmo_> wtf?
[2/25/2006 3:48 PM] <Narada> harr
[2/25/2006 3:48 PM] <Narada> Good 'ol fucked up memory saved me.
[2/25/2006 3:48 PM] <qwertydawom> Yes Elmo, 0 is even :)
[2/25/2006 3:48 PM] <Elmo_> how so?
[2/25/2006 3:48 PM] <Narada> 1 is odd
[2/25/2006 3:48 PM] <Elmo_> That's just following a patern...
[2/25/2006 3:49 PM] <Narada> ... which is what defines if a number is even or odd.
[2/25/2006 3:49 PM] <Narada> I think.
[2/25/2006 3:49 PM] <qwertydawom> yes, but, I'm going to stay a bit on these terms ;)
[2/25/2006 3:49 PM] <qwertydawom> and explain.
[2/25/2006 3:49 PM] <qwertydawom> We say that a number is 'even' if this number is divisible by 2.
[2/25/2006 3:50 PM] <qwertydawom> (or, it is equivalent to say : a number is even if it's a multiple of 2)
[2/25/2006 3:50 PM] <qwertydawom> We say that a number is 'odd' if this number gives a remainder of 1 when divided by 2.
[2/25/2006 3:51 PM] <qwertydawom> (an equivalent statement is : an 'odd' number is a number that is follows an 'even' number)
[2/25/2006 3:51 PM] <qwertydawom> So, if we call 'n' our natural integer, then we can say that :
[2/25/2006 3:52 PM] <qwertydawom> # n is even <==> n = 2*k
[2/25/2006 3:52 PM] <qwertydawom> # n is odd <==> n = 2*k + 1
[2/25/2006 3:52 PM] <qwertydawom> e.g. : 6 is even : 6 = 2*3
[2/25/2006 3:52 PM] <qwertydawom> 7 is odd : 7 = 2*3 + 1
[2/25/2006 3:53 PM] <qwertydawom> These two formulas are the key to understand properties of odd an even numbers! :)
[2/25/2006 3:53 PM] -->| death_in_a_can (death_in_a@bu-5AC87799.sfldmidn.dynamic.covad.net) has joined #lecture
[2/25/2006 3:53 PM] <qwertydawom> So, Elmo, you can see that : 0 = 2*0, hence, 0 is even ;)
[2/25/2006 3:54 PM] <qwertydawom> got it?
[2/25/2006 3:54 PM] <Elmo_> yep
[2/25/2006 3:55 PM] <qwertydawom> Alright, now, let's see basic operations with respect to odd and even numbers
[2/25/2006 3:55 PM] <qwertydawom> 1° Addition (or substraction) !
[2/25/2006 3:56 PM] <qwertydawom> What happens if I add an even number with an other even number?
[2/25/2006 3:56 PM] <qwertydawom> Let's see :
[2/25/2006 3:56 PM] <Elmo_> it'll be an odd
[2/25/2006 3:56 PM] <qwertydawom> 2*k + 2*l = 2*(k+l) = 2*m  (with m = k+l)
[2/25/2006 3:56 PM] <Elmo_> or not
[2/25/2006 3:56 PM] <qwertydawom> So, it'll be an even number.
[2/25/2006 3:57 PM] <qwertydawom> And it will ALWAYS be an even number ;)
[2/25/2006 3:57 PM] <qwertydawom> Thus, Narada, is the following sentence is true? :
[2/25/2006 3:57 PM] <Narada> not again :/
[2/25/2006 3:57 PM] <Ch4r> lmao
[2/25/2006 3:57 PM] <qwertydawom> "An even number added to another even number will give an even number."
[2/25/2006 3:57 PM] <Elmo_> TRUE!
[2/25/2006 3:57 PM] <Elmo_> oops
[2/25/2006 3:58 PM] <Narada> Natural numbers?
[2/25/2006 3:58 PM] <qwertydawom> Yes :)
[2/25/2006 3:58 PM] <Narada> True.
[2/25/2006 3:58 PM] <qwertydawom> w00t!
[2/25/2006 3:58 PM] <qwertydawom> but in fact, it also works if we take relative numbers ;)
[2/25/2006 3:59 PM] <qwertydawom> e.g. : 4 + (-2) = 2 --> even + even = even
[2/25/2006 3:59 PM] <Narada> We just started doing nonreal numbers with calc in my math class :)
[2/25/2006 3:59 PM] <Narada> That funky i symbol.
[2/25/2006 3:59 PM] <qwertydawom> ah yeah :)
[2/25/2006 3:59 PM] <qwertydawom> complex numbers ;)
[2/25/2006 3:59 PM] <qwertydawom> but, that's not the point of this lecture :p
[2/25/2006 4:00 PM] <Elmo_> Narada, what grade are you in?
[2/25/2006 4:00 PM] <Narada> 12
[2/25/2006 4:00 PM] <Elmo_> :O
[2/25/2006 4:00 PM] <Ch4r> keep the random conversation in #binaryuniverse... on with the lecture ;)
[2/25/2006 4:01 PM] <qwertydawom> Ok, so, who can apply my reasoning to the case 'odd + odd'? :)
[2/25/2006 4:02 PM] <Ch4r> = even
[2/25/2006 4:02 PM] <Ch4r> and even + odd = odd... ;/
[2/25/2006 4:03 PM] <qwertydawom> can you prove them? ;)
[2/25/2006 4:03 PM] <Ch4r> uh
[2/25/2006 4:03 PM] <Ch4r> good question;\
[2/25/2006 4:04 PM] <Elmo_> teehee
[2/25/2006 4:04 PM] <qwertydawom> Elmo, can you? :)
[2/25/2006 4:04 PM] <Elmo_> 3 + 3 = 6 || 9 + 9 = 18 = proven
[2/25/2006 4:04 PM] <qwertydawom> no no!
[2/25/2006 4:04 PM] <Elmo_> oh.. you mean mathematically?
[2/25/2006 4:04 PM] <qwertydawom> this is not a proof!
[2/25/2006 4:04 PM] <qwertydawom> yes I do ;)
[2/25/2006 4:05 PM] <Elmo_> 2k-1 + 2l-1 = 2*(k+l)-1 
[2/25/2006 4:05 PM] <Elmo_> or something
[2/25/2006 4:06 PM] <qwertydawom> lol, I told you an odd number was : 2*k+1, so use that :)
[2/25/2006 4:06 PM] <Elmo_> o
[2/25/2006 4:06 PM] <Elmo_> same poop
[2/25/2006 4:06 PM] <qwertydawom> I know it's true that an odd number is : 2*k - 1
[2/25/2006 4:06 PM] <qwertydawom> but, it's better to have "+" than "-" ;)
[2/25/2006 4:06 PM] <Elmo_> 2k+1 + 2k+1 = 2(k+l)+1
[2/25/2006 4:07 PM] <qwertydawom> no!
[2/25/2006 4:07 PM] <Ch4r> hmm...
[2/25/2006 4:07 PM] <qwertydawom> since this would give you : odd + odd = odd, which is not true ;)
[2/25/2006 4:07 PM] <Ch4r> 2k+1 + 2l+1 = 2(k+l)=1?
[2/25/2006 4:07 PM] <Elmo_> i give up... Elmo_ needs cookies
[2/25/2006 4:07 PM] <Ch4r> +1*
[2/25/2006 4:07 PM] <Ch4r> not =
[2/25/2006 4:08 PM] <qwertydawom> that would be the same as Elmo's
[2/25/2006 4:08 PM] <Ch4r> oh ;/
[2/25/2006 4:08 PM] <qwertydawom> Let me do this one ;)
[2/25/2006 4:08 PM] <Elmo_> 2k+1 + 2k+1 = 2(k+l)+2
[2/25/2006 4:08 PM] <Elmo_> because 1+1 = 2
[2/25/2006 4:08 PM] <Elmo_> :-)
[2/25/2006 4:08 PM] <qwertydawom> 2k + 1 + 2l + 1 = 2(k+l+1) = 2m
[2/25/2006 4:08 PM] <qwertydawom> yes, Elmo got the 'trick' ;)
[2/25/2006 4:08 PM] <qwertydawom> So : Odd + odd = even
[2/25/2006 4:08 PM] <Elmo_> Elmo_ got the style 
[2/25/2006 4:09 PM] <qwertydawom> and, Narada knows that this sentence is true ;) :
[2/25/2006 4:09 PM] <Narada> har har
[2/25/2006 4:09 PM] <qwertydawom> "An odd number added with an odd number gives an even number"
[2/25/2006 4:09 PM] <Narada> yup
[2/25/2006 4:10 PM] <qwertydawom> Ok, so now, Elmo, do the 'odd+even' case ;)
[2/25/2006 4:10 PM] <Elmo_> yes sir
[2/25/2006 4:10 PM] <Elmo_> 2k+1 + 2l = 2(k+l+1) = 2m+1
[2/25/2006 4:11 PM] <Elmo_> i hope i'm right
[2/25/2006 4:11 PM] <qwertydawom> your second step is false
[2/25/2006 4:11 PM] <Elmo_> yarr
[2/25/2006 4:11 PM] <Elmo_> oh
[2/25/2006 4:11 PM] <Elmo_> 2(k+l)+1
[2/25/2006 4:11 PM] <Elmo_> because we need 1 not 2 :-)
[2/25/2006 4:12 PM] <qwertydawom> ;)
[2/25/2006 4:12 PM] <qwertydawom> so : odd + even = ?
[2/25/2006 4:12 PM] <Elmo_> odd
[2/25/2006 4:12 PM] <qwertydawom> yep
[2/25/2006 4:12 PM] <qwertydawom> and, since the '+' operator is commutative, we have that :
[2/25/2006 4:12 PM] <qwertydawom> even + odd = odd
[2/25/2006 4:12 PM] <qwertydawom> :)
[2/25/2006 4:12 PM] <Elmo_> short way
[2/25/2006 4:13 PM] <qwertydawom> Yep, so, to sum it up, we have that : the addition of two numbers that are either both odd or both even gives an even number.
[2/25/2006 4:13 PM] <qwertydawom> Does it remind you of some logic operator by any chance? :)
[2/25/2006 4:13 PM] <Elmo_> just like.. NN = P || PP=P
[2/25/2006 4:14 PM] <Elmo_> while NP = N
[2/25/2006 4:14 PM] <qwertydawom> ?
[2/25/2006 4:14 PM] <Elmo_> Negative | Positive
[2/25/2006 4:14 PM] <qwertydawom> a LOGIC operator
[2/25/2006 4:14 PM] <Elmo_> Xor :)
[2/25/2006 4:15 PM] <qwertydawom> Yay! :D
[2/25/2006 4:15 PM] <qwertydawom> So, now, let's study the "multiplication" 
[2/25/2006 4:15 PM] <qwertydawom> What happens if we multiply two even numbers?
[2/25/2006 4:15 PM] <Elmo_> even
[2/25/2006 4:16 PM] <qwertydawom> Well, let's see! :)
[2/25/2006 4:16 PM] <Elmo_> 2 odds : odd
[2/25/2006 4:16 PM] <qwertydawom> 2*k * 2*l = 2(k*l) --> even
[2/25/2006 4:16 PM] <qwertydawom> ahem
[2/25/2006 4:16 PM] <qwertydawom> sorry
[2/25/2006 4:16 PM] <qwertydawom> it should be :
[2/25/2006 4:17 PM] <qwertydawom> 2*k*2*l = 4*k*l = 2*(2*k*l) --> even
[2/25/2006 4:17 PM] <qwertydawom> Now, prove the 'odd * odd' case Elmo ;)
[2/25/2006 4:18 PM] <Elmo_> okay...
[2/25/2006 4:18 PM] <Elmo_> 2k * 2l + 1 = 4kl + 1 = 2(2kl)+1 --> odd
[2/25/2006 4:19 PM] <qwertydawom> no no
[2/25/2006 4:19 PM] <qwertydawom> it's "odd * odd", not "even * odd" :)
[2/25/2006 4:19 PM] <qwertydawom> So :
[2/25/2006 4:19 PM] <Ch4r> 2(k+1)*2(l+1) = 4(kl+2)
[2/25/2006 4:19 PM] <Ch4r> right? ;\
[2/25/2006 4:19 PM] <qwertydawom> ahem, no
[2/25/2006 4:19 PM] <Ch4r> ;o
[2/25/2006 4:20 PM] <qwertydawom> (2k+1)*(2l+1) ;)
[2/25/2006 4:20 PM] <qwertydawom> and, now... FOIL! :)
[2/25/2006 4:20 PM] <Elmo_> w00t!
[2/25/2006 4:20 PM] <Ch4r> >_<
[2/25/2006 4:20 PM] <Ch4r> so..
[2/25/2006 4:21 PM] <Ch4r> 4kl + 2k + 2l + 1...
[2/25/2006 4:21 PM] <Ch4r> hmm
[2/25/2006 4:21 PM] <Elmo_> 4 + 2l + 2 +...
[2/25/2006 4:21 PM] <qwertydawom> Ch4r's got the right one ;)
[2/25/2006 4:21 PM] <Narada> 4lk+2k+2l_1
[2/25/2006 4:22 PM] <Narada> gah too late
[2/25/2006 4:22 PM] <Ch4r> Narada: I win. 
[2/25/2006 4:22 PM] -->| diac_bot (death_in_a@bu-5AC87799.sfldmidn.dynamic.covad.net) has joined #lecture
[2/25/2006 4:22 PM] <Ch4r> ;)
[2/25/2006 4:22 PM] <Narada> :p
[2/25/2006 4:22 PM] <qwertydawom> so : 4kl + 2k + 2l + 1 = 2(2kl + k +l) + 1 --> odd
[2/25/2006 4:22 PM] <qwertydawom> Hence : odd*odd = odd :)
[2/25/2006 4:22 PM] <qwertydawom> And now, who's volunteer for : odd*even? :)
[2/25/2006 4:23 PM] * Elmo_ points a finger to the right.
[2/25/2006 4:23 PM] * Ch4r points a finger to the left
[2/25/2006 4:23 PM] * Narada ducks
[2/25/2006 4:23 PM] <qwertydawom> haha
[2/25/2006 4:23 PM] <Ch4r> Narada: too late :D
[2/25/2006 4:23 PM] <Elmo_> it's you qwertydawom 
[2/25/2006 4:23 PM] <qwertydawom> okay ;P
[2/25/2006 4:24 PM] <qwertydawom> so : (2k+1)*(2l) = 4kl + 2l = 2(2kl + l) --> even :)
[2/25/2006 4:25 PM] <qwertydawom> and now, who tells me why the case 'even*odd' will give the same result?
[2/25/2006 4:25 PM] * Elmo_ is fucking
[2/25/2006 4:25 PM] <Elmo_> ducking*
[2/25/2006 4:25 PM] <Elmo_> damn
[2/25/2006 4:26 PM] <qwertydawom> so?
[2/25/2006 4:27 PM] <Elmo_> i dunno
[2/25/2006 4:27 PM] <Elmo_> because be make the 1 into a 2 by foil
[2/25/2006 4:27 PM] <qwertydawom> no no
[2/25/2006 4:27 PM] <qwertydawom> because... the '*' operator is commutative ;)
[2/25/2006 4:29 PM] <qwertydawom> Ok, so, to sum it up, we have that :
[2/25/2006 4:29 PM] <qwertydawom> Only the multiplication of two odd numbers gives an odd product.
[2/25/2006 4:29 PM] <qwertydawom> Does it remind you of a logic operator? :)
[2/25/2006 4:29 PM] <Elmo_> nor ?
[2/25/2006 4:29 PM] <qwertydawom> nope
[2/25/2006 4:29 PM] <Ch4r> and
[2/25/2006 4:29 PM] <Elmo_> ah
[2/25/2006 4:30 PM] <qwertydawom> yes ch4r ;)
[2/25/2006 4:30 PM] <qwertydawom> and now, we shall see the particular case of the 'square' of a number.
[2/25/2006 4:30 PM] <qwertydawom> I guess you all know what it is?
[2/25/2006 4:31 PM] <Ch4r> yeah
[2/25/2006 4:31 PM] <Elmo_> root?
[2/25/2006 4:31 PM] <qwertydawom> no, just the square :)
[2/25/2006 4:31 PM] <qwertydawom> not the square root
[2/25/2006 4:31 PM] <qwertydawom> e.g. : 2 squared -> 4
[2/25/2006 4:31 PM] <Elmo_> ah
[2/25/2006 4:32 PM] <Elmo_> x * x
[2/25/2006 4:32 PM] <qwertydawom> yes
[2/25/2006 4:32 PM] <Elmo_> cube would be x^x right? (sorry, just a curious equestion)
[2/25/2006 4:32 PM] <qwertydawom> so, what can we say about : even^2
[2/25/2006 4:32 PM] <qwertydawom> no, cube would be : x*x*x :)
[2/25/2006 4:32 PM] <Elmo_> ah
[2/25/2006 4:33 PM] <Elmo_> even^2 = even
[2/25/2006 4:33 PM] <Elmo_> for even * even = even
[2/25/2006 4:33 PM] <Elmo_> if my mind didn't mess up
[2/25/2006 4:33 PM] <Ch4r> don't you dare ask us to prove that qwerty :P
[2/25/2006 4:33 PM] <qwertydawom> haha :)
[2/25/2006 4:34 PM] <qwertydawom> and, what about : odd^2?
[2/25/2006 4:34 PM] <Ch4r> odd
[2/25/2006 4:34 PM] <qwertydawom> yup :)
[2/25/2006 4:35 PM] <qwertydawom> So, we can say that a number squared keeps its odd/evenness :)
[2/25/2006 4:35 PM] <qwertydawom> Now, thanks to Elmo's curiosity, we shall study the case where we take the cube of the number.
[2/25/2006 4:36 PM] <Ch4r> it's the same as squaring a number, yes?
[2/25/2006 4:36 PM] <Ch4r> I mean as far as oddness/evenness
[2/25/2006 4:36 PM] <Elmo_> no?
[2/25/2006 4:36 PM] <Elmo_> oh, yes
[2/25/2006 4:36 PM] <qwertydawom> agreed
[2/25/2006 4:36 PM] <Ch4r> and so is uhh... ^4
[2/25/2006 4:37 PM] <Ch4r> and ^5
[2/25/2006 4:37 PM] <Ch4r> ;x
[2/25/2006 4:37 PM] <qwertydawom> so, Ch4r, what can you tell me about the oddness/evenness of a number raised to the n-th power? :)
[2/25/2006 4:37 PM] <Ch4r> the oddness/evenness of n is the same as n to any power :p
[2/25/2006 4:38 PM] <qwertydawom> w00t! :)
[2/25/2006 4:38 PM] <Ch4r> if the power is greater than 0
[2/25/2006 4:38 PM] <Ch4r> right/
[2/25/2006 4:38 PM] <Ch4r> ?*
[2/25/2006 4:38 PM] <Ch4r> cuz 8^0 != even
[2/25/2006 4:38 PM] <qwertydawom> yep :)
[2/25/2006 4:38 PM] <qwertydawom> since : n^0 = 1 -> odd ;)
[2/25/2006 4:39 PM] <qwertydawom> Alright now, tell me which other operation we're missing?
[2/25/2006 4:40 PM] <Ch4r> hmm
[2/25/2006 4:40 PM] <qwertydawom> So far we've covered : addition, substraction, multiplication
[2/25/2006 4:40 PM] <Ch4r> and division, haven't we?
[2/25/2006 4:40 PM] <Ch4r> and exponents..
[2/25/2006 4:41 PM] <qwertydawom> no, we haven't discussed division :)
[2/25/2006 4:41 PM] <Ch4r> oh >_<
[2/25/2006 4:43 PM] <qwertydawom> So, let's do it now ;)
[2/25/2006 4:43 PM] <qwertydawom> What happens if we divide two even numbers?
[2/25/2006 4:43 PM] <qwertydawom> 2k/2l = k/l, can we conclude?
[2/25/2006 4:44 PM] <Elmo_> odd
[2/25/2006 4:44 PM] <Ch4r> or even
[2/25/2006 4:44 PM] <Ch4r> either... O.o
[2/25/2006 4:44 PM] <Elmo_> yeah...
[2/25/2006 4:44 PM] <Ch4r> because, for instance, 24/12 = 2, which is even, but 24/24 = 1, which is odd :P
[2/25/2006 4:45 PM] <Elmo_> well
[2/25/2006 4:45 PM] <Elmo_> excluding the number its self...
[2/25/2006 4:45 PM] <Elmo_> 24 / 12 = 2 24 / 6 = 4 24 / 4 = 6...
[2/25/2006 4:45 PM] <Elmo_> so.. it's always even UNLESS its the number devided by its self
[2/25/2006 4:45 PM] <Elmo_> right qwertydawom ?
[2/25/2006 4:45 PM] <Ch4r> hmm
[2/25/2006 4:45 PM] <qwertydawom> no :)
[2/25/2006 4:45 PM] <Elmo_> damn
[2/25/2006 4:45 PM] <Ch4r> fractions..
[2/25/2006 4:46 PM] <Ch4r> ;x
[2/25/2006 4:46 PM] <qwertydawom> we CANNOT conclude ;)
[2/25/2006 4:46 PM] [INFO] Now logging to <file:///C:/Documents%20and%20Settings/Administrator/Application%20Data/Mozilla/Firefox/Profiles/qvfvh6ty.default/chatzilla/logs/irc.binaryuniverse.net/channels/%23lecture.2006-02-25.log>.
[2/25/2006 4:46 PM] [INFO] Channel view for ``#lecture'' opened.
[2/25/2006 4:46 PM] -->| YOU (D31337) have joined #lecture
[2/25/2006 4:46 PM] =-= Topic for #lecture is ``Next logic lecture: Saturday, February 25th at 9 PM GMT +0 | /join #binaryuniverse''
[2/25/2006 4:46 PM] =-= Topic for #lecture was set by Ch4r on Sunday, February 19, 2006 7:16:08 PM
[2/25/2006 4:46 PM] <Ch4r> ok
[2/25/2006 4:46 PM] <Ch4r> good
[2/25/2006 4:47 PM] <Elmo_> yep
[2/25/2006 4:47 PM] <Narada> I think I already am.
[2/25/2006 4:47 PM] <Ch4r> for odd/odd, we can't conclude
[2/25/2006 4:47 PM] <Ch4r> Narada, ok, cool
[2/25/2006 4:47 PM] <Narada> shit, i'm not
[2/25/2006 4:47 PM] <Narada> i'll just copy and paste
[2/25/2006 4:47 PM] <Ch4r> it's ok
[2/25/2006 4:47 PM] <Ch4r> Delly logged
[2/25/2006 4:47 PM] -->| nslain (nslain@bu-144BB6A8.hsd1.mn.comcast.net) has joined #lecture
[2/25/2006 4:47 PM] <Narada> k
[2/25/2006 4:47 PM] <qwertydawom> yes Ch4r, we can't conclude :)
[2/25/2006 4:47 PM] <qwertydawom> and, what about : odd/even, even/odd?
[2/25/2006 4:48 PM] <Ch4r> we can't conclude ;o
[2/25/2006 4:48 PM] <Elmo_> devision sucks... it's so unconstant
[2/25/2006 4:48 PM] <qwertydawom> aye
[2/25/2006 4:48 PM] <qwertydawom> Now, Elmo, you talked about the 'square root'
[2/25/2006 4:48 PM] <qwertydawom> What about it?
[2/25/2006 4:48 PM] <qwertydawom> sqrt(even)?
[2/25/2006 4:48 PM] <qwertydawom> sqrt(odd)?
[2/25/2006 4:49 PM] <Narada> Are evens even and odds odd?
[2/25/2006 4:50 PM] <qwertydawom> sqrt(2)? :p
[2/25/2006 4:50 PM] <Narada> gah
[2/25/2006 4:50 PM] <Elmo_> sqrt(even) = odd
[2/25/2006 4:50 PM] <Ch4r> nah
[2/25/2006 4:50 PM] <Elmo_> sqrt(81) = 9
[2/25/2006 4:50 PM] <Elmo_> even = even
[2/25/2006 4:50 PM] <Elmo_> teehee
[2/25/2006 4:51 PM] <qwertydawom> no
[2/25/2006 4:51 PM] <Ch4r> since x^2 has the same evenness/oddness as x, the square root of x^2 has to have the same evennness/oddness as x^2...
[2/25/2006 4:52 PM] <Elmo_> cannot conclude?
[2/25/2006 4:52 PM] <qwertydawom> elmo's right ;)
[2/25/2006 4:52 PM] <Narada> Ch4r: that's what i thought
[2/25/2006 4:52 PM] <Ch4r> oh wait...
[2/25/2006 4:52 PM] <Ch4r> yeah, I see
[2/25/2006 4:52 PM] <qwertydawom> Ch4r, you know what's wrong? :)
[2/25/2006 4:52 PM] <Ch4r> yeah, I see.
[2/25/2006 4:52 PM] * Narada explodes.
[2/25/2006 4:52 PM] <qwertydawom> It's a simple implication ;)
[2/25/2006 4:52 PM] <qwertydawom> x even/odd => x^2 even/odd :)
[2/25/2006 4:55 PM] <Ch4r> gotcha..
[2/25/2006 4:56 PM] <qwertydawom> in fact, your reasoning would work with integers ;)
[2/25/2006 4:56 PM] <qwertydawom> if we know that n is the square of an integer
[2/25/2006 4:57 PM] <qwertydawom> then, we can say that sqrt(n) has the same evenness/oddness than n :)
[2/25/2006 4:57 PM] <qwertydawom> ok?
[2/25/2006 4:58 PM] <Ch4r> mhm
[2/25/2006 4:59 PM] <qwertydawom> e.g. : "4 is the square of an integer", so, we know that sqrt(4) will be even :)
[2/25/2006 5:02 PM] * Ch4r waits :p
[2/25/2006 5:03 PM] <qwertydawom> Ok lol
[2/25/2006 5:03 PM] <qwertydawom> So, we've seen that we couldn't conclude with the square root
[2/25/2006 5:05 PM] <qwertydawom> And, this ends this (long) parenthesis about odd and even numbers ;)
[2/25/2006 5:05 PM] <qwertydawom> Now, let's get back to the concept of 'truth'
[2/25/2006 5:06 PM] <qwertydawom> There are some statements whose truth is yet to be proven.
[2/25/2006 5:07 PM] <qwertydawom> For example, if I ask... guess who? Yes, Narada! (;)), if the following statement is true :
[2/25/2006 5:07 PM] <Narada> aw snaps
[2/25/2006 5:07 PM] <qwertydawom> "Every even number can be written as the sum of two prime numbers"
[2/25/2006 5:07 PM] <qwertydawom> I guess you all know what a prime number is?
[2/25/2006 5:07 PM] <Narada> yeah
[2/25/2006 5:07 PM] <Narada> hmm
[2/25/2006 5:08 PM] <Elmo_>  true
[2/25/2006 5:08 PM] <qwertydawom> Well, using computers, it has been checked that statement up to a really big number, and it SEEMS to be true.
[2/25/2006 5:08 PM] <Narada> agreed
[2/25/2006 5:09 PM] <Narada> seems?
[2/25/2006 5:09 PM] <qwertydawom> But, it has not yet been proved (mathematically) that it was right. :)
[2/25/2006 5:09 PM] =-= Elmo_ is now known as Elmo-afk
[2/25/2006 5:09 PM] <qwertydawom> This is still an open question.
[2/25/2006 5:09 PM] <qwertydawom> So, if you guys can prove this is always true, you can get some money ;)
[2/25/2006 5:09 PM] <Elmo-afk> how much?
[2/25/2006 5:09 PM] <Narada> lol
[2/25/2006 5:10 PM] =-= Mode #lecture +v death_in_a_can by qwertydawom
[2/25/2006 5:10 PM] <Ch4r> hmm
[2/25/2006 5:10 PM] <qwertydawom> Well, this is known as "Goldbach's conjecture" ;)
[2/25/2006 5:11 PM] <qwertydawom> For those of you who're interested : http://en.wikipedia.org/wiki/Goldbach's_conjecture
[2/25/2006 5:11 PM] <Ch4r> 2 is considered prime, yes/
[2/25/2006 5:11 PM] <Ch4r> ?*
[2/25/2006 5:11 PM] <qwertydawom> yes :)
[2/25/2006 5:12 PM] <qwertydawom> the prime numbers are numbers that are only divisible by 1 and themselves.
[2/25/2006 5:12 PM] <Ch4r> so it seems like all even numbers could be written as sums of 2s, and all odd ones could be written as the sum of 2s and 3s ;/
[2/25/2006 5:12 PM] <qwertydawom> By definition, 1 isn't prime.
[2/25/2006 5:12 PM] <Ch4r> wheres the flaw in my logic? ;o
[2/25/2006 5:13 PM] <death_in_a_can> thats valid logic
[2/25/2006 5:13 PM] <death_in_a_can> but the question asked for sum of only 2 numbers
[2/25/2006 5:13 PM] <Ch4r> oh
[2/25/2006 5:13 PM] <qwertydawom> yes :)
[2/25/2006 5:13 PM] <Ch4r> whoops
[2/25/2006 5:13 PM] <Ch4r> my bad
[2/25/2006 5:13 PM] <qwertydawom> no problem ;)
[2/25/2006 5:15 PM] <qwertydawom> So, in this lecture, we have seen how important the concept of truth was in mathematics.