# ∞/2= ∞?

1. Aug 5, 2011

∞/2= ∞

Please comment. I do not thnk this is right.

2. Aug 5, 2011

### HallsofIvy

Staff Emeritus
What number system are you working in? Strictly speaking, in the real number system, there is no "$\infty$" but you can think of that as "shorthand" for $\lim_{x\to\infty} x/2$. In that case, yes, that limit is $\infty$.

And, in any number system in which $\infty$ is defined as a number (extended reals, for example) it is true that $\infty/ 2= \infty$.

3. Aug 5, 2011

Is there any logical or math problem with the value of ∞ in this question? Does the value of ∞ change?

4. Aug 5, 2011

### Mentallic

Why not? What would you expect a never ending number which is halved to be?

5. Aug 6, 2011

### Hurkyl

Staff Emeritus
No. ∞ = ∞. Why do you think ∞/2 should have a different value from ∞?

(my assumption for this post: we are working in the extended real numbers or projective real numbers)

Most likely answer: you are trying to apply your intuition about algebra of real numbers. But ∞ isn't a member of the real numbers, and so it can behave differently -- and this particular algebraic behavior is one example of that different behavior.

If you actually think about what ∞ is defined to be or what sorts of things it can quantify ∞=∞/2 should actually be rather obviously true.