I'm having an issue proving the statement in the title. In particular looking at the proof at https://ncatlab.org/nlab/show/sequentially+compact+metric+spaces+are+totally+bounded I don't get how we can state that the sub-sequence doesn't converge given that the distance between two points of the sequence must be greater than epslion.
Thank you in advance
So the problem asks to show if the following set is sequentially compact or not and to say why:
{x in R: e^x - x^2 <= 2}
I simply rearranged terms and rewrote the above as f(x) = e^x - x^2 -2 <= 0. I noticed that by looking at the graph of the derivative, f'(x) > 0 and thus the function is strictly increasing so the above set would be unbounded and therefore not be sequentially compact. Is there way to show this without using a graph? A question like this may pop on on my exam next week and I'm not sure how to justify this without a graph.
American builds are just always huge and usually poorly built. I suppose I could build my own, but I work 6 day a week from 7 to 7. I have money and would gladly buy a nice prebuilt but its rare.
It just seems like a glaring open space in the market place. if I had the motivation I would develop and sell small vans with living capabilities.
As someone who has lived in a car for some time its not hard. Have one place to stand. Have a small portable toilet . And have some kind of climate control. Those features cost less than 3K to install.
The models in the US cost over 100k, this is insane. And they arent even built well. Hence the surge of home built camper vans like on this sub.
In europe you can buy an excellent van sized RV for less than 50K, they still make a profit.
Im just mad.. and want to escape on the weekends without having to drive a semi or having to spend half my life savings.
edit: american companies used to build campers like I described decades ago, but for some reason not any longer? I honeslty dont care if its from the US, if Japan was still selling their campers from the 90's I would absolutely buy... There is just no good affordable prebuilts. and some entrepreneur could make alot of money if done right.
Edit 2: because I've had to repeat it so many times. Standing room, a toilet and climate control.. its basic
Sometimes I wish I was stocky 5'6 so I can learn a compact powerful form and then return to my original build (6'3 180). I'm plateauing a bit right now around 375-400 max (besides the "griplock" bombs I posted about a while ago) and I'm still looking for the sauce. I feel like I can hit 375-400 in spite of my form, not because of it. I'm tall, athletic, and I have thrown a lot of frisbees in my day. I can make a disc move. But I'm still feeling clumsy and inconsistent. I know some would love to hit 400, but I feel disappointed by it. First-world problems? I just know there's more in the tank that I'm not using consistently and its frustrating. I often feel like I have too much moving at once, I'm not compact enough, and I'm not consistently using my long-levered "advantage". I have a theory that tall lanky folk have more room for error because of the space our motion takes up. Maybe I'm just making up an excuse :-). Either way, I'm in form rebuild mode currently and my head is spinning.
Tall lanky disc golfers, what are some things you have discovered about being tall and lanky throwin discs? If anything, is there anything you've done to fix/improve/take advantage of your lanky-limbed Gumby motion?
