Thread: ~~Time Number Theory~

Originally posted by stovellp
12:08

1 + 2 + 0 + 8 = 11
12 + 08 = 20
2 + 0 = 2

Doesn't work out.....

Umm...
1 + 2 + 0 + 8 = 11
1 + 1 = 2
12 + 08 = 20
2 + 0 = 2

OK, here's a proof that I made (I had nothing to do; I had to shut down the computer due to a thunderstorm )
It proves that King Zoolerius ther ory is correct for any two number os any length in any base.

S(X) is the digit sum of X
B is the base

If X is a number of length n in base B, X can be written as
X = B^0 * x0 + B^1 * x1 + ... + B^n * xn
then S(X) is calculated as follows
S(X) = S(x0+x1+...+xn) if X >= B (*)
S(X) = X if X<B

Now, if we choose two arbitrary numbers X and Y, if King Zoolerius' theory is correct, then:
S(X+Y) = S(x0+x1+...+xn + y0+y1+...+yn)

S(X+Y) = S[ B^0*(x0+y0) + B^1*(x1+y1) + ... + B^n*(xn+yn) ]
but we earlier concluded (*) that this could we written as
S(x0+y0+x1+y1+...+xn+yn)which is just what we was going to show.


This has obviously nothing to do with base 10, here's an example with hexadecimal numbers:
X = EF361AA
Y = 518204B
E+F+3+6+1+A+A + 5+1+8+2+0+4+B = 5A and 5+A = F
EF361AA + 518204B = 140B81F5 and 1+4+0+B+8+1+F+5 = 2D and 2+D = F

Originally posted by stovellp
But thats doing it differently. The first example he gave only split the second number (the 12+06) but didn't split the first number (1+2+0+6).

You cannot split a single digit (9), can you?
You split every number larger than of equal to the current base.

Finally!, someone who supports and agrees with my theory!! I love you Sang-drax!!!

Huzzah, SangDrax. Good job.