Sure I could be wrong but when I looked at the problem as a statistical thermodynamics model it became apparent that the numbers in this system would always tend towards being reduced until eventually equaling one since there is a shrinkage of 0.5 for each power of two totaling infinity, plus a 1 that we can basically ignore since the growth of odd numbers becomes 2.5x = (0.5 x) * 3 + 1 and 2.5x is much smaller than infinity.

(edit: Ok, maybe it’s 3x since the +1 is insignificant and can be ignored, but it’s still less than infinity)

This is my solution @ youtube https://www.youtube.com/watch?v=5mFpVDpKX70

Sorry I’ve been away but it is impossible to blog without the IRS or NSA harassing you, I decided it’s better to just wait until a certain criminal out of office before I blog. Yeah, gag order, keep your mouth shut or get audited and have your computer filled with NSA spyware, gotta love this communism!

So how did we get here?

It wasn’t fun…

0.5x * 2 = 1x (damn)

0.25x * 4 = 1x (damn)

Doh, they all needed to be summed.

2^-2 x * 2 = 0.5x (shrinkage)

2^-4 x * 4 = 0.5x (shrinkage)

2^-8 x * 8 = 0.5x (shrinkage)

….

2^(infinity) * infinity = 1x (shrinkage)

=

(Infinity * 0.5 + 1) x (shrinkage)

That’s infinite shrinkage is much bigger than our 3X growth!

I guess I proved it instead of cracking it? Who knows, it’s 6am and I haven’t yet had any sleep because of my asthma.6

Well I edited my post, 6am commenting isn’t all it’s cracked up to be…

This must be important because NSASOFT rebooted my computer before I could answer that this is a statistical problem that must be looked at as one would look at thermodynamics. Half of all numbers are odd (0.5x), every number multiplied by an odd number is an odd number and every odd number plus 1 is an even number, so we can just say that the dynamics of this system leads to a growth of 0.5x * 3 + 1 = 2.5x (edit: actually 3x since the 1 becomes insignificant but still less than infinity, read on). But we are seeing a shrinkage, why? 0.5x * 2 = 1x is clearly smaller than 2.5x (or 3x) but when we replace 0.5 with z, and 2 with y it becomes apparent that for the first two even numbers in the sequence (2 and 4) we end up with z/2 * x * y = 0.5 and z/2 * x * 2y = 1, we divide z by two because half of the even numbers will be divisible by 4 and half of them won’t, we can repeat this process for the next power of two and what happens is the each power of 2 adds 0.5 to the total, and the sum accumulation of 0.5 for each of the infinite number of power of two’s is infinity therefore the system will always tend to the smaller number which becomes 1 since 1 * 3 + 1 = 4 > 4/2 = 2, 2/2 = 1, once a number becomes 1 it is stuck there forever, so totals will float around the system until they are stuck at 1. For even numbers we’re summing {z/2 * x * y = 0.5} an infinite number of times and adding 1 to the total since z/2 * x * 2y = 1. Crazy but true.

Can I name the unit of the final terms 3X and (Infinity + 1)X as statistical inflation/deflation? Sure it’s some imaginary concept that only exists in the realm of the theoretical. For this to be proof than one must say that an infinite statistical deflation implies an inability for the system to enter a stagnant state that doesn’t deflate BUT we’re talking about an infinite deflation, with NO stable states other than 1 and infinity, 2 and 3 are both prime numbers and from RNG’s I pretty much assume that the numbers are basically random and won’t enter a stagnant state. Will I take this to the next level and prove that /2 and *3 lead to a RNG? No way! I should have minded my own business, but at least the NSA and IRS have something to read on my blog.

For those who say I have a tin foil hat, I assure you that I received a letter from the IRS, and I have skype installed, nuff said.