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
But
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?
$\infty / \infty$
) 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. $\endgroup$