/sci/ - Science & Math

>>11645380
Based and Goodstein-pilled

>>11426507
You have a sequence. A sequence can be thought of as a function f that assigns a number f(n)=a_n for any given natural number n. Now for the definition of convergence: Sequences converge to a value a' if and only if for any arbitrarily small number ε, you can find some corresponding number (usually quite large) N with the property that if you pick any n' greater than N, then the difference between f(n') and a' is less than the small number ε. Basically, the sequence gets bounded by ε past N. I've just restated the definition in slightly different language, but hopefully it is more clear. If you still don't understand, then just stare at your book's or my definition for a long time till it clicks.