In some cases, life itself becomes one big bad experience, and people don’t want to do anything. It seems the good times should give one traction to continue; but over time; in some people; the angst of bad times overwhelms the remains of positive results.

]]>Now for sum of my recent discoveries(part of this was discovered by someone else) based upon simple formulas try this:

take the numbers 1 to 9 123456789 , then add the two numbers next to each other 1+2 you get three then 2+3 = 5 , 3+4 =7 ,4+5 =9 5+6=11 digit root = 2 and keep going. you get:

123456789

357924681

837261594

219876543

318642975

495162738

.

.

. continue further until the sequence ends at row 18 and a pattern appears when arranged in a grid. pattern shown more clear:

12 3 45 6 789

3 57 9 24 6 81

8 3 72 6 15 9 4

21 9 87 6 54 3

3 18 6 42 9 75

4 9 51 6 27 3 8

etc.. pattern shown 33966 diagonally

there are more proofs to be uncovered but i’ll start with this for now. And i do not use this to claim this as has anything to do with healing or free energy(cause there’s no such thing). Its just simple equations with interesting patterns as far i go so far. ILLUMINATI CONFIRMED hehe ðŸ™‚

If you can break this pattern, Mark, you’ll get 10 gold stars from me.

]]>Given any two real numbers a and b, if a =/= b, then WLOG, a > b (otherwise, just swap a and b over). Therefore, a – b > 0. Since the sequence (1/2^n) convergest to 0 and is positive for all n, there is some N such that 0 < 1/2^N < (a – b). Now, there are integers c and d such that c/2^N ** a (the former since (-n/2^N) tends to minus infinity as n tends to infinity, and the latter since (n/2^N) tends to infinity as n tends to infinity). Obviously, d > c, so the set of integers c such that c/2^N **** b (else c* would not be maximal), and (c* + 1)/2^N = c*/2^N + 1/2^N < b + 1/2^N < b + (a – b) = a, so b < (c^* + 1)/2^N < a, and (c^* + 1)/2^N is rational since both 2^N and c^* + 1 are integers.**

Do you mind listing category theory books/articles you like?

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