Can infinite recurrence be mathematically proven?

[Opoint]

Hi, I would like to tell the room I’m a novice. I know very little math, mostly Algebra. So asking these questions in themselves are over my head. But I have a question that I wonder can be shown mathematically. I want to know if there can be an infinite recurrence. (For all I know it could be a little syntax or symbol) – denoting such an action.

This was my first post on this forum. Please elaborate if you know the answer.

 

[Opoint]

Perhaps I wasn’t precise enough. You see, I’m seeking a number known as zero. And this quality is seen in math more than anywhere else. Perhaps this observation is best said in the philosophy room. But I’m going to give it a go in here instead (since I believe it COULD be represented mathematically) and this room is for math.

To continue my initial thought the ‘infinite recurrence’ Idea: largely this number is undefined. But so is dividing by 0: so the undefined is definable… as simply unsolvable.

Further, I have a thought in my mind regarding the number zero (perhaps only mathematical zero) –As it is related to recurrence. In other words, zero must recur an infinite amount of times and still remain 0 (in order for it to be defined as 0). But, at what point does recurrence make complexity? (This we may never know) If zero can indeed recur an infinite amount of times… it would then follow it was infinitely complex.

I know this is a big homework problem. But please try and respond to this.

 

[berkeman]

Do you mean like in an infinite series?

$$\sum^{\infty}_{1} \frac{1}{x^2}$$

And with your infinite sum of zeros?

$$\sum^{\infty}_{1} 0$$