So much of math..........like e...............is one more...............(1 + 1/n)^n.........................2 broken in half.................like 1/2..................

So...........taking the 1st nine fractions..........from 1/2 to 1/10...............there are 9 of them.................a jump from single to double digit denominators............imp also.............b/c 6 of them do not overlap..........................6.................like 1/6....................like 1.618...........the golden ratio..............................1/2 + 1/4 + 1/8 + 1/16...........is how the halving series starts..............the next fraction is 1/3..................................like the primes themselves.............how they start............2, 3.................also like the line at 1/2..............b/c 1/2 is the 1st overtone.....................taking the denominator like an exponent.............................1/3 is next...............as an "original" geo series................b/c the halving series..........based on the 1st overtone........1st fraction does not produce 1/3..............3 is prime after all............u cannot multiply up to it by a whole number..............




“Nonsense, you gullible old toad!” you are perhaps shouting to your screen. “Why should throwing out the numbers with 9’s make such a difference? We’ve still got all the other numbers!”
Again, I say: not so fast. You’re making a classic mistake. When you think of “numbers,” you’re only picturing little numbers.
“No I’m not!” you may say. “I’m thinking of big numbers. Huge numbers. Like 9 million, or 47 billion, or 228 trillion.”
Exactly my point: small numbers.
You see, the longer a number gets, the harder it is to avoid a 9. Every time you add a digit, you add a new opportunity for a 9. That might not feel like a big danger—after all, those 9’s will pop up only 10% of the time. But look what happens: