So infinity is clearly a very strange, concept.

So I have the following proposal (the nick lim proposal) which can not be solved ( at least to my current knowledge, hopefully you can shed some light ).

For the following scenarios since I do not have an infinity character on my keyboard, replace x with the infinity symbol.

What is x/x?

Well we know 2x = x

So we could rewrite x/x = 2x/x

Well 2x/x

Well in that scenario x/x = x


lets flip that around

2x = x so x/x = x/2x

In this scenario x/x = 1/2 //Think of limits imagine y/2y as y approaches infinity it's 1/2.

So it seems x/x = "1/k where k is all positive integers" or "just x"

Edit: 1.1x = x and 1.5x = x and .1x = x

So x/x = "1/k where k is all positive real numbers" or "just x"

What do you think?

  • 1
    $\begingroup$ $\infty/\infty$ (obtained by writing $\infty / \infty$) is what is known as an indeterminate form, much like $0/0$. You can make it become whatever you wish, but in specific settings, it is very possible that it has a specific value. $\endgroup$
    – Arthur
    Nov 5, 2015 at 21:09
  • $\begingroup$ But in my explanation isn't that not true? It can only be a certain number of values that are determinate? $\endgroup$
    – Novaly
    Nov 5, 2015 at 21:11
  • 2
    $\begingroup$ Also down voting this question is ridiculous, if you disagree you can simply post or comment. $\endgroup$
    – Novaly
    Nov 5, 2015 at 21:12
  • 1
    $\begingroup$ The problem here is that you are trying to treat $\infty$ as if it were an ordinary number, which it is not. Pushing symbols around without regard to their meaning generally results in nonsense. "Garbage in, garbage out." $\endgroup$
    – MPW
    Nov 5, 2015 at 21:12
  • 1
    $\begingroup$ There's no math in your question, I'm afraid. Jotting down symbols and saying something like “we know $2\infty=\infty$” is not doing mathematics. To a statement such as “$\infty/\infty=1/k$ where $k$ is all positive numbers“ I cannot attribute any sensible meaning. Are you really surprised about two downvotes? I'm surprised there aren't more, to be honest. No, I didn't downvote. $\endgroup$
    – egreg
    Nov 5, 2015 at 22:36

2 Answers 2


What would you think of the reasonning " $0 \times 1 = 0 \times 2$ so $1 = 2$" ? Both products $= 0$, so you can't simplify.

Similarily $\infty \times 1 = \infty \times 2$ cannot implies 1 = 2 for the same reason: both products are infinity, so you can't simplify.


$\infty$ is the limit of t at infinity. $\infty$ is also the limit of 2t at infinity.

When you write $\frac \infty \infty$, there is no reason that both $\infty$ are set to the same sequence, each could freely map to any sequence going to infinity. That's why the result is indeterminated, and that's why your reasonning is flawed.

  • $\begingroup$ but in the form 2t/t as t approaches infinity the limit would be two because the top grows twice as quick as the bottom considering you can never GET to infinity correct? $\endgroup$
    – Novaly
    Nov 6, 2015 at 3:56
  • $\begingroup$ yes the form 2t/t as t approaches infinity the limit would be two (ideed it's 2 at any time) . Just, it is totally wrong to pretend that writting $\frac {2\infty} \infty$ is equivalent to writting this limit (I explained why many times above). $\endgroup$ Nov 6, 2015 at 8:11
  • $\begingroup$ 2infinity/1infinity, lets cancel the infinities that equals 2/1 $\endgroup$
    – Novaly
    Nov 6, 2015 at 9:26
  • $\begingroup$ No. not in maths, not in science. We spent hour here to explain you why. But if you don't accept any math/science argument, it'd your freedom to decided to create a brand new different mathematics elsewhere that in a math forum. $\endgroup$ Nov 6, 2015 at 14:20

Not the answer you're looking for? Browse other questions tagged .