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.