About 0/0

There is a proof that \( \frac{0}{0}\) is indeterminate because:
If you divide 0 by tiny positive numbers approaching 0, the answers approach \(+♾\).
And If you divide 0 by big negative numbers approaching 0, the answers approach \(♾\).
Then \( \frac {0}{0}\) is indeterminate because it can’t be \(+♾\) and \(♾\) at the same time.
Assuming this is true, why can’t \( \frac{0}{0}\) be \(+♾\)? 
What would +♾ mean anyway?
