Dividing Infinity by Infinity: What is the Result?

[adjacent]

What would happen if,I divide ∞ by ∞.What would be the answer. Would it be 1?

 

[phinds]

If would be undefined.

 

[adjacent]

If would be undefined.

I don't understand,What do you mean?

 

[hilbert2]

Infinity is not a number and you can't calculate with it like you can with usual numbers. Consider the values of quotients \frac{x+1}{2x+1} and \frac{2x+1}{3x+1} when $x$ is let to grow without bound. In both expressions the numerator and denumerator approach infinity when $x\rightarrow\infty$, but the value of first expression approaches $1/2$ and the value of second expression approaches $2/3$. You can't define a unique value for the quotient $\infty/\infty$.

 

[phinds]

I don't understand,What do you mean?

What is it about the word "undefined" that you do not understand? It means "would have no definition". Is that not clear?

 

[HallsofIvy]

In terms of "ordinary arithmetic", "infinity" is NOT a number and so there simply is NO definition for "infinity over infinity". There are ways of extending the number systems to give various types of "infinity" some of which then allow you to divide infinity by infinity. Most of those, but possibly not all, define division so that infinity by infinity is 1.