MAA 3200 Midterm: MAA 3200 FIU Exam 313k
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Prof. s. hudson: [20 pts] answer true or false. Assume that s and t are non-empty, bounded sets in. R, and that (g, ) is a group. If g is isomorphic to an abelian group h, then g is also abelian. If g is abelian, then is commutative and associative. glb s < lub s. The set { 1, 1} r, with multiplication, forms a group. If s [3, 5] then s has an accumulation point x, with x 5. If l =lub rng (xn) exists, then lim xn = l. In q, every cauchy seq is bounded. lub (s t ) = min { lub s, lub t }. If x is an accumulation point of s then some sequence xn s converges to x: [10 pts] choose one. Note that 2b is a bit harder and may net 5 extra points. 2a) [10 pts] show that if n, xn 0 and l = lim xn then l 0.
