Is iteration process through equal sign possible? Is iteration process through equal sign possible?
for an example: repeatedly pressing on the equal button of calculator

Repeatedly pressing on the equal button of calculator until full converging the Answer.

this is (Ahmad Reza Estakhr's) symbol of iteration of equal sign $\Re_{i=1}^{\infty}=$ which means repeatedly pressing on equal sign.
 A: That just depends on what the equal sign on your calculator is programmed to do.
Usually the equal sign is meant to compute as much as it can (in your terms, carry out as many "iterations" in one step as possible) - if you type in 5+(3*2)+8+9, it will return 28, instead of returning 5+6+8+9.
It's possible, yes, for certain cases (e.g. if your calculator is a polynomial solver), especially if your equal sign is programmed to carry out simplification; however, by and large, it will just land you returning the same value over and over again. In other words, the general answer to your question is no.
A: The answer is: yes, probably, subject to a few caveats. Here are two I can think of:


*

*it must be running an algorithm that will actually converge (it's sometimes rather hard to prove that an algorithm converges with a given input, e.g. Newton-Raphson with a given polynomial and 'starting value'),

*it must be performing an algorithm that isn't very sensitive to rounding errors (because calculators will make them!).


But there are probably more.
A: yes, it is possible, 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.
