Alright, I’ll explain it myself. I was expecting someone to say it’s because $ = 1 and c = 0.01, which is wrong.
Lets schedule a couple of those linear equations regarding the relation between $ and c:
1$ - 100c = 0
0.01$ - 1c = 0
↓ THEREFORE
[code] – –
| 1 -100 | 0 |
| 0.01 -1 | 0 |
L2 => (-L1/100 + L2)
| 1 -100 | 0 |
| 0 0 | 0 |
0$ + 0c = 0
0 = 0[/code]
“Sweet, Bruno, what does this mean?”
That you can’t define $ if you don’t have c, and you can’t define c if you don’t know $. That means $ isn’t necessarily 1: all we know is, it’s worth 100 c. So if 1 c is worth 5 in pure numbers, 1 $ equals 500.
“Alright, and what’s the difference?”
The difference is, since $ and c can’t be defined in terms of pure numbers, they’re said to be a number system. As a number system, it doesn’t matter how much $ is worth, what matters is $ is the basic unit of its system, so it’s worth 1 of whatever we’re measuring with it. Although $ doesn’t have to equal 1, $ α 100% (α indicates proportionality) of it’s system, whilst c α 1%.
Thus, the issue can be demonstrated as follows:
1 $ α 100%
1 c α 1%
↓ TO THE POWER OF 2
1² $² α (100%)²
1² c² α (1%)²
↓ THEREFORE
1 $² α 100%
1 c² α 0.01%
↓ THEREFORE
1 $² = 1 $
1 c² = 0.01 c
There’s a lot of nice psyched metaphysical stuff one can find out from that, a real lot, but I really don’t have the time for the crazy what the metaphysics.
Now, as promised:
x = ³√8
x³ -8 = 0 → 2³ -8 = 0
2 = 2∙(cos 0 + i sen 0)
By Euler’s fomula,
2 = 2∙e^(i 0)
Since the other two solutions must be spread around the complex field with argument 2 and equal angular distances, we divide 2π/3 and get the three solutions:
[b]α = 2∙e^(i ⅓∙2π)
β = 2∙e^(i ⅔∙2π)
γ = 2∙e^(i 2π)[/b]
↓ THEREFORE
S = { 2∙e^(i ⅓∙2π), 2∙e^(i ⅔∙2π), 2∙e^(i 2π) }
Wow that was fast!
Someone else propose a problem!