# i want reference about the method(below) of describing Infinity… [closed]

let think x is real number, then \begin{align} x&=x\\ x&=(x/2)+(x/2), \\ x&=(x/3)+(x/3)+(x/3), \\ x&=(x/4)+(x/4)+(x/4)+(x/4), \\ &\vdots \\ x&=(x/n)+(x/n)+(x/n)+ \cdots +(x/n), \\ \end{align} If $$n$$ is too large and equal to infinity, then

$$x=(x/\infty)+(x/\infty)+(x/\infty)+(x/\infty)+\cdots+(x/\infty)$$

then

$$(x/\infty)= \epsilon$$ and this $$\epsilon$$ is equal ant to zero. Because in goes below planck scale and we can't observe it. my question is that who described it?

## closed as off-topic by Riccardo.Alestra, Claude Leibovici, Strants, jgon, GNUSupporter 8964民主女神 地下教會Mar 26 at 14:03

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• Welcome to Math.SE! Please format your question using MathJax. This page should give you a start at learning how to typeset mathematics here so that your posts say what you want them to, and also look good. – Brian Mar 26 at 12:32
• Planck scale is a physical properties of the space - time. You refere to a mathematical assumption about infinity – Riccardo.Alestra Mar 26 at 12:36
• That seems weird. What does Planck length have to do with real numbers? We don't need to observe real numbers, in order to calculate with them. – Matti P. Mar 26 at 12:36
• What your describing looks a lot like non-standard analysis, for which I once wrote a good introduction: universiteitleiden.nl/binaries/content/assets/science/mi/…. Let me know if anything's unclear. – Floris Claassens Mar 26 at 12:57

I do not believe a reliable reference can be found since the method you describe is inherently flawed. The value $$n$$ is never "equal to" $$\infty$$. Likewise, there is no such number as "$$(x/\infty)$$," and it is most certainly not equal to 0.
Rather, it would appear that you are attempting to evaluate the limit of the series $$\sum_{i=1}^{n}\frac{1}{n}$$ as $$n$$ approaches $$\infty$$ by treating the series as
$$\lim_{n\to\infty}\sum_{i=1}^{n}\frac{1}{n} = \sum_{i=1}^{n}\lim_{n\to\infty}\frac{1}{n} = \underbrace{\lim_{n\to\infty}\frac{1}{n} +\lim_{n\to\infty}\frac{1}{n} + \cdots + \lim_{n\to\infty}\frac{1}{n}}_{n\ \text{times}}$$ which is nonsensical, since the number of elements in the series depend the value of $$n$$, which no longer "exists" outside of the sum.
You may find the answers to this semi-related question helpful, which concludes that $$1=2$$ by computing $$\frac{\mathrm d}{\mathrm d x}x^2 = \frac{\mathrm d}{\mathrm d x} \underbrace{x+x+\cdots+x}_{x \ \text{times}}$$