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Not only is the symbol daunting, but the words are too

by flyingpig
Tags: daunting, symbol, words
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micromass
#37
Sep26-11, 08:01 PM
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OK, so that is indeed correct. We indeed have that

1 + (0 + 1) = (1 + 0) + 1 = 0

But that is not were the error was. The error is in the following

1 + (1 + 0) = (1 + 1) + 0 = 1 + 0 = 1

So can you calculate

1+(1+0)=...
(1+1)+0=...

again and see where the error is?
flyingpig
#38
Sep26-11, 08:04 PM
P: 2,568
Quote Quote by micromass View Post

So can you calculate

1+(1+0)=...
(1+1)+0=...

again and see where the error is?
But they all arrive at the same answer

1 + (1 + 0) = 1 + 1 = 0

(1 + 1) + 0 = 0 + 0 = 0

But 1 + (1 + 0) from A2 says 1 + (1 + 0) = (1 + 1) + 0 = 0 + 0

I don't see the error
micromass
#39
Sep26-11, 08:12 PM
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Quote Quote by flyingpig View Post
But they all arrive at the same answer

1 + (1 + 0) = 1 + 1 = 0

(1 + 1) + 0 = 0 + 0 = 0

But 1 + (1 + 0) from A2 says 1 + (1 + 0) = (1 + 1) + 0 = 0 + 0

I don't see the error
Indeed, they are all 0. But before you said that it was equal to 1. So now you have the correct answer.
flyingpig
#40
Sep26-11, 08:14 PM
P: 2,568
Impossible I had 0!!! It was in post#29!!!

Oh well at least I got the other 7 right! ahahhaah

Wait, does that mean I will have 8 x 8 = 64 lines to write for all the other ones...?
flyingpig
#41
Sep26-11, 08:17 PM
P: 2,568
Correction * 64
micromass
#42
Sep26-11, 08:19 PM
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Yes, now try to do the other ones. This should be quite easy if you understood this one.
flyingpig
#43
Sep26-11, 08:20 PM
P: 2,568
oH MY GOD, Please stay with me in case I made a silly mistake. With 64, I will...
flyingpig
#44
Sep26-11, 08:25 PM
P: 2,568
A1 done, A2 speaks for itself.

Quote Quote by A2

x + y = y + x

Let x = 0, y = 0

0 + 0 = 0 + 0 = 0

Let x = 0, y = 1

0 + 1 = 1 + 0 = 1

Let x = 1, y = 0

1 + 0 = 0 + 1 = 1

Let x = 1, y = 1

1 + 1 = 1 + 1 = 0
OKay probably not 64 then

Quote Quote by A3

I sense danger from this one...

x + 0 = x

Let x = 0

0 + 0 = 0

[b]Let x = 1[/tex]

1 + 0 = 1
Quote Quote by A4
x + (-x) = 0

Oh boy

Let x = 0

0 + (-0) = 0 + 0 = 0

Let x = 1

1 + (-1) =....
Stuck already...I am an idiot

DOing M1-M4 D in another post.
micromass
#45
Sep26-11, 08:33 PM
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OK, for A4, you need to use that -1=1 and -0=0. You define this to be so.
flyingpig
#46
Sep26-11, 08:40 PM
P: 2,568
Quote Quote by M1
Damn it, 8 cases again

(xy)z = x(yz)

Let x = 0, y = 0, z = 0

(0*0)0 = 0(0*0) = 0*0 = 0

Let x = 0, y = 0, z = 1

(0*0)1 = 0(0*1) = 0*0 = 1

Let x = 0, y = 1, z = 0

(0*1)0 = 0(1*0) = 0*0 = 0

Let x = 1, y = 0, z = 0

(1*0)*0 = 1(0*0) = 1*0 = 0

Let x = 1, y = 1, z = 0

(1*1)0 = 1(1*0) = 1*0 = 0

Let x = 1, y = 0, z = 1

(1*0)1 = 1(0*1) = 1*0 = 0

Let x = 0, y =1, z = 1

(0*1)1 = 0(1*1) = 0*1 = 0


Let x = 1, y = 1, z = 1

(1*1)1 = 1(1*1) = 1*1 = 1
Quote Quote by M2

xy = yx

Let x = 0, y = 0

0*0 = 0*0 = 0

Let x = 0, y = 1

0*1 = 1*0 = 0

Let x = 1, y = 0

1*0 = 0*1 = 0

Let x = 1, y = 1

1*1 = 1*1 = 1
Quote Quote by M3

Other than 0, there is a 1 such that x * 1 = x

Let x = 0

0 * 1 = 0

Let x = 1

1*1 = 1
Quote Quote by M4

Other than 0, we have an inverse for x

Oh wait...should I just do x = 1 case...?
Quote Quote by D

NOOO ANOTHER 8 CASE. I'll be back on this one...
Need water...be back in 2 mins.
micromass
#47
Sep26-11, 08:43 PM
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The second of M1 is incorrect.
flyingpig
#48
Sep26-11, 09:01 PM
P: 2,568
Yes because 0*0 is not 1...!

Quote Quote by D

Let x = 0, y = 0, z = 0

0(0 + 0) = 0*0 + 0*0 = 0 + 0 = 0

Let x = 0, y = 0, z = 1

0(0 + 1) = 0*0 + 0*1 = 0 + 0 = 0

Let x = 0, y =1, z = 0

0(1 + 0) = 0*1 + 0*0 = 0 + 0 = 0

Let x = 1, y = 0, z = 0

1(0 + 0) = 1*0 + 1*0 = 0 + 0 = 0

Let x = 1, y = 1, z = 0

1(1 + 0) 1*1 + 1*0 = 1 + 0 = 1

Let x = 1, y = 0, z = 1

1(0 + 1) = 1*0 + 1*1 = 0 + 1 = 1

Let x = 0, y = 1, z = 1

0(1 + 1) = 0*1 + 0*1 = 0 + 0 = 0

Let x = 1, y = 1, z = 1

1(1 + 1) = 1*1 + 1*1 = 1 + 1 = 0
I am pretty confident in this one
micromass
#49
Sep26-11, 09:08 PM
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Looks ok!!
flyingpig
#50
Sep26-11, 09:09 PM
P: 2,568
Now just imagine I have to put all of this on paper.
flyingpig
#51
Sep26-11, 09:53 PM
P: 2,568
Quote Quote by SammyS View Post
For this field, -1 = 1 . This is because the thing you need to add to 1 to give you the identity element for addition is 1.
Quote Quote by micromass View Post
OK, for A4, you need to use that -1=1 and -0=0. You define this to be so.
I overlooked something. since WHEN DID I DEFINE -1 = 1?
micromass
#52
Sep26-11, 09:55 PM
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Well, you need to find for each x, an element y such that

x+y=0

By definition, this element is -x.

So, for x=0, you need an element such that 0+y=0. When you look at the axioms, you see that y=0 is the only possibility. So -0=0.

Now, what is -1?
flyingpig
#53
Sep26-11, 09:58 PM
P: 2,568
Oh is it from 1 + 1 = 0, that 1 = -1? oh okay
micromass
#54
Sep26-11, 09:58 PM
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Quote Quote by flyingpig View Post
Oh is it from 1 + 1 = 0, that 1 = -1? oh okay
Yes.


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