/sci/ - Science & Math

30 mathematical geniuses have committed suicide trying to solve the equation of infinity. They became obsessed and so have I. How can something exist that has no beginning or no end...no start and no finish. For those who it is too hard to comprehend, think of the concept of God.

30 mathematical geniuses have committed suicide trying to solve the equation of infinity. They became obsessed and so have I. How can something exist that has no beginning or no end...no start and no finish. For those who it is too hard to comprehend, think of the concept of God.

30 mathematical geniuses have committed suicide trying to solve the equation of infinity. They became obsessed and so have I. How can something exist that has no beginning or no end...no start and no finish. For those who it is too hard to comprehend, think of the concept of God.

Alright guys, so we were discussing the concept of infinity in maths class the other day, and my mind started drifting off. What ended up happening was that I thought of this thought experiment I believe to be a paradox.

I explained it to my teacher, who said he didn't think it was a paradox, although he was unable to explain why. I was hoping any of you could help me resolve this, or explain to me where my line of thinking is going wrong.

So, without further ado, here's the thought experiment:

1. We have access to a machine which selects a random number between 0 and ∞.
2. We run the machine once, and we get a number. We will call this number X1.
3. We run the machine again. This time we get a number we will call X2.
4. The chances that X2 will be smaller than or equal to X1 are infinitely small, as there are an infinite amount of larger numbers that could be chosen but only a finite amount of smaller numbers.
5. This goes for all following results; X3, X4, X5, X6 etc.
6. Hence, we would expect to get a sequence of numbers getting progressively larger.
7. However, all these numbers are chosen independently of each other, and are all equally random, so it seems odd that we should get a pattern of this sort.

I don't know how to explain this any better, and I haven't seen anyone else do a similar thought experiment before. In my mind, it seems to be a paradox. Thanks for your help if you decide to respond.

infinity is just a theory right?
in order for an infinite number to be represented in reality, the universe would need to be infinite... yeah?

if a number can be represented, than that number is no longer infinite correct?
so it would have to be a theory, which is unprovable...right?
so Pi cannot be an endless number...
also, why do we use rounding? its a one way process and depending on the complexity of the algorithm, the resulting answer would be significantly different if you rounded a number than if you didnt round.

>>im not well educated, and learn as i go..so go lightly on me?

Would I be right in thinking that the number of polygons is aleph-1, while that of regular polygons is only aleph-null?