Ok so first I am doing to divulge background information, of myself with everyone. Yeah, I do think it is important but if you do not care, skip this
next paragraph.
I love math. I am in high school and I understand that I know nothing. I have taken basic Physics, Advanced Chemistry, Advanced Statistics, as well as
Calculus II (my favorite subject ever). I sit at my desk for fun and contemplate math and everything that exists conceptually within it. Generally,
these periods of fun generally end in me writing a 5-10 page essay of my thoughts. Unfortunately, threads that I have authored about math generally
end up with people telling me I have no idea what I am talking about and that, basically, I am trying to be smarter than I really am. One, day, I hope
I do know a great deal of math. I am going to go to Colorado School of Mines and become a Physicist. I WANT to know things. I think of things that
many times scare me, involving math. I try to theorize and, well, I have no place to do so when I know nothing. Here is where ATS will help me, I hope
Ok, so I just wrote a thread not too long ago, in which I was trying to describe how I believe some infinities must, in concept, be larger than
others. Within this thread came up the dilemma of 1/∞, and how I think it must equal 0.
Now I am versed very well in calculus and understand the concept of limits very well. A limit merely tries to show in a graph what
appears to
happen, even though it may not actually occur. So if you find a limit of something, you are using math to show what is going to happen at a point
where there is a hole in the graph, an asymptote, or maybe even how you think the graph will behave after a long (a very long or even infinite) period
of time.
A good introduction to limits
A deeper understanding of limits, and how to evaluate them
Now, the question is: what happens to 1 when it is divided by infinity? Well you can look at it graphically in the example of y=1/x, and take a look
at the limit of y when x approaches ∞. Well, you end up realizing that the limit is zero. So does this mean that 1/∞ equals 0? Well according to
many people, the answer is no. 1/∞ is undefined and actually equals a number that is (relatively equivalent to) 0.0(repeating)1. Well this makes
sense, and you cannot dispute this, really in any way that I know of.
But I say, what if you pretend that an infinite time has passed for y, and that we pretend that x actually
does equal infinity? Then, wouldn't
be look at the limit, and assume that because the limit as x approaches infinity equals zero that if we reached infinity, it would be equal to
zero?
Now, we cannot treat infinity as a number--I get that. It has no numerical value and is really more of a concept than anything. It cannot be treated
as a number, but can still be examined, IMO as one, in math (you do this informally with
L'Hospital's Rule all the time).
Here is a good explanation of infinity, through diagrams
So I have tried to put together some basic information of infinity, but I have also come across some very complex explanations of the "plane of
infinity". I most want to explore this aspect of math, because I think it will help me grasp what I am trying to communicate with the difference of
infinities, and the imaginative prospect of actually looking at something as it exists in an infinite state...
So, ATS, wanna help? I need some people to go through with me and others here to decipher this math and help clear things up once and for all. Here
are the links to what I am talking about, clear explanation on any of them are useful:
Projective Infinity
Transfinite Numbers and Set Theory
Line at Infinity
Point at Infinity
My biggest priority here is to understand. I hope others can respect my mathematical ignorance, I have a desire to know though.
Also, here are my failed attempts at trying to know something if anyone is interested in furthering their mathematical thoughts:
Limits at Infinity, the number 1 is bigger than you may think
Clarification on Time and What Creates it (*Note, this one was written within my first
week or so of Calculus so the math part isn't the most beautiful of things.
edit on 18-3-2012 by PhysicsAdept because: (no reason
given)