Wednesday, March 27, 2024

consecutive number theory is approximate

I had been working on consecutive number theory. I did not have relevant journals, books or a guru sitting beside me all these time. And I had deep mathematical thoughts. For example, I nearly reached Wallis pi in 2010. So what I did was explore mathematics as consecutive numbers theory. This was the best option. Also because I was alone most of the time.

I applied my thoughts on consecutive numbers. I made rational number series. I made 3 consecutive and 4 consecutive number theory. I got easy pi expressions. Easy because the partial sums were easy. 

It is "strange" that x squared decreases when x is less than 1 and greater than 0. Similarly x cubed, x to the power of 4 and so on. Euler and English mathematicians had expressions for this factor. In their e and log functions. Essentially what came across was decimal factorials. Decimal factorial exists and they "explain" the fact that x^n decreases when x is between 1 and 0.

Is consecutive numbers able to explain this phenomenon? x^n decreases when x is less than 1 and greater than zero? Also the decimal factorials?

In an approximate way, yes.

All in all, a man can truly explain the beauty and logic of the nature. Approximately. With his fingers.

That is all for now.

Have a great day ahead !! 


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