Thread replies: 3
Thread images: 1
Thread images: 1
I was sitting in a boring lecture about triple integrals when I realized this. First, the trivial shit.
Step 1: The number 1 generates a group of order 1 with multiplication. That is because 1 times 1 = 1, so it is closed. The other properties follow trivially.
Step 2: The number -1 generates a group of order 2. This is because (-1)^2 = 1, and (-1)^3 = -1. You probably already know this.
Step 3: i generates a group of order 4. Now the sequence goes i,-1,-i,1,...
And you probably already saw this as an example in a group theory textbook. But here comes THE FUCKING KICKER.
Let [math] \phi = \sqrt{i} [/math]. Now the sequences fucking goes:
[math] \phi , i ,\phi i ,-1 , - \phi, -i, -\phi i,1[/math]
And now [math] \phi [/math] generates a group of order 8!. But I could now take the square root of phi and get a group of order 16.
Holy fucking shit.
>>
>>8961173
I am going to go kill myself now...
I want this to be on my gravestone.
"It was trivial."
>>
You're just taking smaller slices of the "unit circle" in C. 1=e^(i*2pi), -1=e^(i*pi), i = e^(i*(1/2)pi), etc.
Thread posts: 3
Thread images: 1
Thread images: 1