pg. 2 exchange supremum and infimum. pg. 3 switch the inequalities for Holder and Minkowski (but not the words). In the RHS, multiplication and addition should be switched. R_0^n should be a separate bullet point. pg. 4 The topological definition of closure: containing E, not contained in E. pg. 5 Compact subsets of *metric spaces* are closed. If K is a *metric space*, K is compact iff sequentially compact. pg. 6 Nested nonempty *closed* sets F_n pg. 8 every bounded subsequence of R^k should be every *sequence* of R^k. for should be form. pg. 9 The "n->infty" should be after inf/sup. 3-3: if the sequence is eventually positive, not not equivalent to the 0 sequence. pg. 10 Ratio test, 2nd bullet should be > pg.12 definition of continuity should have d(x,p)0 not t->x. pg. 16 Sums should start at k=0. f(beta)=P(alpha)+... 0<=k=\epsilon, not <\epsilon pg. 22 Delete 2nd-to-last paragraph of 7-1. pg. 23 Item 2: define g_n=g_{n,n} Item 3: Delete "For this N_i". Add to end of sentence, for $k,l>=N$. Weierstrass approximation. Replace f:[a,b]\to C with f:[a,b]\to R. P_n(x)-f(x): The integral after this, f should be \bar{f}. In statement of Stone-Weierstraa "function" should be "functions" pg. 25 In proof of Taylor, sum b_n should be sum b_nx^n. (i.e. has a limit point... should be (i.e. E has a limit point. f(x)=0 in a neighborhood of f(x)\in E should be f(x)\not\equiv 0 in a neighborhood of x_0.