For example, $$\frac{1}{1}=1\quad \frac{1}{2}=0.5\quad \frac{1}{3}=0.\overline3\quad \frac{1}{10}=0.1$$ so the larger the denominator is, the smaller the number is.
Would this mean that $\frac{1}{\infty}=0$, or what else could it be?
Also, $$\frac{1}{0.5}=2\quad \frac{1}{0.\overline3}=3\quad \frac{1}{0.1}=10\quad \frac{1}{0.001}=1000$$ and so on. As the numbers in the denominator get smaller, the value of the answer gets larger.
This leads me to the conclusion that $\frac{1}{0}=\infty$. Would this be correct?
I made a comment to your post, but let me add this counterexample:
Let's say infinity was a number, $\infty$. Well we know by definition that for any natural numbers $n$ and $m$ (say $n=3$ and $m=5$), $$3\infty = 5\infty$$ And if infinity is a number, we divide on both sides to get $$3=5$$ In fact it is very easy to come up with examples like this. Reason being is that infinity is a concept of what happens in the limit when you approach something