# Could infinity have a numerical value?

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?

• + or - infinity ? – M. Di Feb 12 '19 at 16:24
• Short answer: no. Any value you try will destroy some important algebraic identity - usually the distributive law. There are many questions on this site asking the same thing. math.stackexchange.com/questions/260876/… – Ethan Bolker Feb 12 '19 at 16:24
• Your examples sort of answer the question. It's that infinity itself is a concept of limiting behavior. There is no value to give to infinity, because by definition it is the characterization of "what happens when you get closer and closer to something" – NazimJ Feb 12 '19 at 16:29

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