Paradox? What's wrong with this thinking?

Question

Let $x = 2 \times 2 \times 2 \times 2 \times 2 \times \cdots$

Thus, $x = 2x \Rightarrow x = 0$

So, $2 \times 2 \times 2 \times 2 \times 2 \times \cdots = 0$

---

This clearly doesn't make any sense. What's wrong then?

Thank you in advance.

Answer 1

It is possible to have products of an infinite number of factors in a hyperreal number system. However, the infinite number, say $H$, is a specific one not equal to $H+1$. Therefore your $x=\prod_{i=1}^H 2$ is not equal to $2x=\prod_{i=1}^{H+1}2$ and the paradox disappears.