**Q:** In the extended real number system, why can't we define: oo+(-oo)=0?

**A:** Because then we could prove that oo+(-oo)=7 by using associativity.
**A:** 1) oo+(-oo)=0

**A:** 2) 7+[ oo+(-oo) ] = 7 + 0

**A:** 3) [7 + oo] + (-oo) = 7

**A:** 4) oo + (-oo) = 7

**Q:** Investigate the uniform convergence of

**Q:** f[n](x) = sqrt(n) * x * (1-x*x)^n on [0,1].

**A:** No uniform convergence on [0,1].

**A:** Use: x[n] = 1 / sqrt(n)

**A:** If 0<M<1, then uniform convergence on [M,1].

**Q:** What is a ring of sets?

**A:** Let X be a set. Let R c P(X).

**A:** R is a ring of sets

**A:** iff

**A:** (1) R is nonempty

**A:** (2) A,B :- R => A u B :- R

**A:** (3) A,B :- R => A \ B :- R

**Q:** Let a[n] be a decreasing sequence of positive numbers.

**Q:** (1) the series a[n] converges

**Q:** (2) the series 2^k * a[2^k] converges

**Q:** Prove that (1) <=> (2).

**A:** page 58 in the first analysis notebook

**Q:** Express differently:

**Q:** max(x,y) = ???