I found a linear algebra question and found Gone's answer interesting , but I didn't really understand it. I'd usually comment asking for a clarification, but apparently Gone who was once Bill has been suspended. So can I open a new question to ask about this answer?

Here is a link to the question : Is there a quick proof as to why the vector space of $\mathbb{R}$ over $\mathbb{Q}$ is infinite-dimensional?

Thank you