The God Function?

Question

Let the function f(x,n,j) equal 1 when for a sequence of integers x of length n there is also a sequence of the same integer of length n+1 contained in some real number j and zero when this is not true. (For example, f(9,2,pi)=1 because there is a sequence of 2 9s at about the hundreth decimal place.)

Let the function f(x,n,j) be given in the form of a triple infinte series:

f(x,n,j) = lim ∑ ∑ ∑a(x,q) + b(n,w) + c(j,e),
summation →∞

where the varibles q, w and e are indicies of summation. Let the functions a, b and c be continuous everywhere.

(a) Is it true that

lim ∂f/∂j = k, k < ∞ ?
j→∞

(b) Is it true that for intervals (0, j) , (j+1, j+2), etc, that the following inequalities are always true?
j
∫f(x,j,n) dj <
0

2j
∫f(x,j,n) dj < ... n→∞
j

Answer 1

God has definitely blessed you with intelligence. I am no where near as cerebral as you are. But I am a good person, I love my kids, and I am not afraid to ask you,,, If you ever win a million dollars can I please have 5 Thousand, to pay off my rat crap car, and buy my kids some clothes.
God Bless,,, and oooh rahh Marine Corps.

Answer 2

Your definition of f is very unclear.

You don't explain why a, b, and c exist.

I could nitpick further, but I suggest you fix those two things for starters.