Math on the Equal Button of Calculator.

Solving polynomials of higher-degree through trial and error method by repeated pressing on the Equal button (=) of Calculator.

\Re_{i=1}^{\infty}=

Sometimes the Answer is a part of Question. for example:

\lim_{n\to Ans} (1+\frac {1}{n})^n=n

Iteration of Equal sign

so you’ve to try repeatedly pressing on the equal button of calculator until full converging the answer.

(1+\frac {1}{Ans})^{Ans}\Re_{i=1}^{\infty}=Ans

n=2.293166287

Ans which means Answer and \Re_{i=1}^{\infty}= which means repeatedly pressing on the equal button of calculator.

Through this trial and error method it is possible to solve problems which is impossible to solve through mathematical methods.

Answer types in this method:
1. Converging Answer
2. Converging Answer require change in equation.(which means answer converge through a special condition)
3. Converging several Answers.
4. Converging No Answer.

For example M-set z_{n+1}=z_{n}^2+c in term of Estakhr’s Iteration symbol is this like:

Ans^2+c\Re_{i=1}^{\infty}=Ans

Interestingly M-set under Estakhr’s iteration equation of the complex quadratic polynomial Ans^2+c\Re_{i=1}^{\infty}=Ans remains bounded, that which means M-set remains bounded (because of imaginary number) but it does not converge to a limit.
Usually the equal sign is meant to compute as much as it can (in this terms, carry out as many iterations in one step as possible, It’s possible, (e.g. if your calculator is a polynomial solver), especially if your equal sign is programmed to carry out simplification.

External link:Fixed point (mathematics)

author: Mr. ESTAKHR, Ahmad Reza

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About easteinstein

I am a physicist with experience of thousands physicists.
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