¹/_Ï€=¹⁰/_31.4159...=¹⁰⁰/_314.159...=...=^∞/_∞=1
¹/_Ï€=¹/₁=1
∴π=1
I hate 0 and ∞...
EDIT: Note that this was a pain to type on an IPhone.

I don't get it.

To keep the ratio correct, wouldn't it have to be 1/π = 1x/(xπ) where -∞<x<∞? So π != 1.

You are right; so what Person has put up is an incorrect evaluation of the limit of 1x/xπ as x-> ∞, which requires L'Hopital's rule. the derivative (in terms of x) of the top over the derivative of the bottom is 1/π.

by the original argument, all numbers equal one. hopefully that's wrong.

I do not understand what was incorrect in my evaluation.

You treated infinity like a single, defined value. It is not. Because of this, you can't just say that ∞/∞=1, because it pretty much never is (and when it does, you've usually just gone on a long excisable detour). In fact, infinity is best treated as a direction. All the infinities are in that direction, but some of them are farther along than others, and there's no way to tell just by looking at them whether one infinity is farther than another.

So how do we compare infinities, if we can't tell by looking at them? We look at what generated them. That is the entire purpose of L'Hôpital's rule.

But since your expression doesn't contain any variables, we can't use L'hôpital's rule, either. So where does that leave us? With one inexorable truth: 1/π will always be 1/π, as long as you do the same thing to both parts of the fraction. Multiplication by zero, by the way, would give us 0/0, which leads us right back to L'hôpital's rule.

However, all I am doing is multiplying both sides by infinity. ... Wait! So infinity isn't a constant? Thus ∞≠∞ which doesn't really made sense... How can you have undefinable end for a limit?

Correct.

I'm a little shaky as to the reasons, but take a look at this. A series can be viewed as the limit of a sum as the number of terms approaches infinite. so like limit (n->∞)∑(1/n) and you get infinity because it does not converge or approach one value. that makes it undefinable as a limit but it can be defined at distinct points.

The problem of zero and infinity in fractions was the reason for this rule which you should read about if you have not already.

EDIT: as far as i understand, everything can be written as a series.

Everything for which a derivative exists can be written as a series.

Things without derivatives (such as Cantor's ternary set) do not always have series definitions, but may have other definitions of similar forms (such as an iterated union).

so is there a general form that includes all these? (series, iterated union, etc)

What you have done is correct up to some extent but there is no perfect solution to prove this and 0 is very important number without zero counting is not possible.
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