I'm having issues with the following concept. I'm sure a problem using the following definition will be on the test on Friday, and I'm not understanding this definition.



Let (Sn), (n in the natural numbers) be a sequence in the real numbers, and s be an element in the real numbers. Then (Sn) converges to s if for ever epsilon>0, there exists some N in the real numbers, such that, for all n in the natural numbers, n>N implies |Sn-s|<epsilon.



I'm not seeing where the N in the reals, n>N matters or comes into play. This definition is causing me a lot of issues. I just don't get it. Could someone explain this conceptually to me?

Don't take real analysis

Fuck, I just read an easy example and it actually makes sense.



Whether I can prove anything worth a damn is a different story, but at least I'm getting it.



When you have Sn, you set that as strictly less than epsilon. Then, you solve for n, and set the other side equal to N.



Hell yes.





 

Umm, 87?

I was hoping to one day make it through advanced mathematics but lost interest 1/2 way through the first line. Good luck.

It finally "clicked".



About damned time, since the test is friday.