what symbol allows you to start at a number, repeat an expression a curtain amount of times, but just sets a variable instead of summing the answer?

Question

This is very difficult to explain, but what I'm looking for, is kind of like sigma but instead I want the middle to do something like this "x=n+1" instead of doing (n+1)+(n+1)+(n+... etc. etc.

So, as an explanation, I am in short trying to recreate the exponent symbol function following these requirements;

• All defined blocks should start with variable "value" [0] and end with an updated value in the main value variable.
• All instructions must never contain "if" or "if/else" statements when referring to the actual math problem.
• All instructions that require prior defined blocks must never use the main value until the end value is calculated, to which it must be stored in the variable "value" as its last action.
• All Instructions may not use math related operation blocks from the editor, and should instead solve the operation/expression using only priorly made defined blocks. (Aside from addition being the only exception in creating the first defined block.)
• All instructions must be composed of numerical results, and must never be built off of results such as; NaN, or infinity.

After attempting to follow all of my self guidelines, I came up with this ridiculous calculation that only works if it had the ability to set variables rather than sum them like sigma does. but for the sake of visualization, I used sigma as a representation of what I'm trying to do.

The "v=" bit on the summation portion is just a visual representation of what I'm trying to do. does anybody know if there is a symbol meant for this? or some other method I could use?

Answer 1

I think you mean iterating a function (continuing the comments)

Say we have $f(x) = x^2 - 1$, and let’s say we start at a number, $x=\pi$.

Now, to repeat that operation, we iterate the function, which basically means plugging $f$ into $f$ like this:

$$f(f(\pi)) = f(\pi^2 - 1)$$

Usually to repeat something $n$ times we have some handy notation:

$$\underbrace{f(f(\cdots f(x))\cdots}_{n \text{ } f \text{ signs}} = f^n (x)$$

However Desmos doesn’t support $f^n (x)$ notation, so we have to just write $f(f(f(\cdots$.

Here’s how you could do it in desmos (this is the app, not the website but I think they are same):