(This was asked due to the comments and downvotes on this Stackoverflow answer. I am not that good at maths, so was wondering if I had made any basic mistakes)
Ignoring limits, I would like to know if this is a valid explanation for why $\frac00$ is undefined:
$x = \frac00$
$x \cdot 0 = 0$Hence There are an infinite number of values for $x$ as anything multiplied by $0$ is $0$.
However, it seems to have got comments, with two general themes.
Once is that you lose the values of $x$ by multiplying by $0$.
The other is that the last line is:
$x \cdot 0 = \frac00 \cdot 0$
as it involves a division by $0$.
Is there any merit to either argument? More to the point, are there any major flaws in my explanation and is there a better way of showing why $\frac00$ is undefined?