Skip to main content

My First Theorem

It's not everyday that I get to exercise my brain in a theoretical fashion, but today was special. I suppose a cosmic ray zapped that one neuron that was holding the rest of them back. Or maybe that cosmic ray zapped too many of those neurons, and now I am delusional about my own grandeur.

Anyway, I have a theory about numbers. Take any integer number and add up its digits. That means for a number like '123' you add '1 + 2 + 3'. My first theory is that the resulting sum will have no more than N-1 digits, where N is the number of digits in the original number. That's nothing new. Call this the DSUM operator.

Now for my conjecture:
(1) Given any number, X, define Y = DSUM(X).
(2) For every Y[i] = DSUM(Y[i-1]), the number of digits in Y[i] will be less than in Y[i-1].
(3) [i] will always be less than or equal to N, where N is the number of digits in X.
(4) For all Y[i], Y[i] is always less than Y[i-1].
(5) There always exists a value of Y[i] such that Y[i] is less than 10.

Now let's do some examples.

X = 123
Y[1] = 1 + 2 + 3 = 6

X = 94567
Y[1] = 9 + 4 + 5 + 6 + 7 = 31
Y[2] = 3 + 1 = 4

X = 0.13598
Y[1] = 1 + 3 + 5 + 9 + 8 = 26
Y[2] = 8

For fractional numbers, (4) does not hold, so it has to be inverted. Y[i] is always greater than Y[i-1].


Yeah fun with numbers. So you read it here first, and I'm off to be famous.

Popular posts from this blog

A Self Defeating Race False Narrative

2020 is the year of the pandemic. The SARS-Cov-2 (Covid19) virus has rampaged across the planet infecting 4,893,136 [1] people by May 20, 2020. At this time, of those 4.8M people, 323,256 people have perished from complications that arise from the infection. Arising out of this pandemic has been a narrative about non-white ethnic groups being disproportionately affected by the infection [6,7,8]. A narrative that conditions people to believe that they are perpetually victims only creates a "collective victimhood" [4,5] in that group. This "collective victimhood" costs its members millions in unrealized potential, sends them cowering from social interactions that would otherwise benefit them, and ultimately creates an environment that perpetuates itself. Let's try to dispel that false narrative and deal just with data. I pulled my data from the CDC [9] looking at mortality only. The mortality data from CDC contains per-state mortality rates on a per-infectio...
Read more

Number of Primes

Anderson's Theorem (a) The number of primes in [1,n] is no more than 2+floor(n/2). The probability of n being prime when n is not prime is 1/2 - see Dasgupta,Papadimitriou,Vazirani "Algorithms" page 26. Therefore, the E(pi(n)) is n/2. (b) There does not exist another set of adjacent primes other than {1,2,3} 5: 2 + floor(5/2) = 2 + 2 = 4:=> {1,2,3,5} : 4 <= 4 7: 2 + floor(7/2) = 2 + 3 = 5 => {1,2,3,5,7} : 5 <= 5 11: 2 + floor(11/2) = 2 + 5 = 7 => {1,2,3,5,7,11} 6 <= 7 26: 2 + floor(26/2) = 15 => {1,2,3,5,7,11,13,17,19,23} : 10 <= 15 Lagrange's Theorem is Inaccurate Lagrange's theorem about primes states that pi(x) is the number of primes <= x. The pi(x) is approximately x/ln(x). He postulated that the lim of pi(x)/(x/lnx) as x-> infinity was 1. This is incorrect. if the number of primes is bounded by n/2 then refactoring and reducing Lagrange's Theorem results in the lim of ln(x) as x approaches infinity. This is alwa...
Read more

Stock Option Debt Income

The 2024 Presidential election has brought out a topic of interest that seems to have been perverted. There is this "Taxing Unrealized Capital Gains" [1] movement that is being falsely attributed to Vice President Harris. Clearly, this is a change in the revenue code that was designed by someone in office long before VP Harris was in office. My money is on Elizabeth Warren and Bernie Sanders. What is this change in the revenue code though? For that you have to understand what Silicon Valley zillionaires are doing with their stock options. Many of these people in this special economic area have huge discounts on stock prices for companies that are not public yet, or are public and can not be sold [2]. To be fair to these holders of equity, banks allow them to finance debt using leverage against those options. If you hold an option that is worth $5M then a bank might lend you a share of that value, thus realizing a debt against the option [3]. This is a fair debt instrument and...
Read more