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) = ???
A: max(x,y) = ( x + y + |x - y| ) / 2
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