Recall def. of a < b and show... a + r < b + r

Related BrainMass Solutions

• Intro CS using Python

  return 3*(x+1) def t(x): """ t computes thrice its input plus one ** and shows how python is more precise than English input x: any number (int or float) """ return 3*x + 1 def r(x,y): """ r

• Intro CS Using Python Program

  Explain in a sentence or two why your answer is the shortest possible. " - f (0, r ( t ( t (0)), t(w(0)) ) ) Using "return (b-1) * (b-2) " or calling f (0, 8) shortens the number of function calls.

• Ideals of a Ring : Containment and Subgroups

  Show that J is an ideal in the ring I (Recall that any ideal of a ring is also a subring; so I is a ring in its own right) Note that: To show J an ideal of I, we must show that 1) it is an additive subgroup of R and 2) it is satisfied

• Portfolio and Stocks

  A portfolio consists of 80 shares of IBM, each costing $150 and 200 shares of GM, each worth $80. For IBM, E(R) = 0.1 and σ(R)= 0.2; for GM E(R) = 0.12 and σ(R)= 0.25. The correlation coefficient between the two companies is 0.75.

• intersection of normal subgroups is a normal subgroup

  439733 Solvable Groups If G is a finite group, define R = R(G) = INTERSECTION {K < G | G/K is solvable}. a. Show that R is the smallest normal subgroup of G, such that G/R is solvable. b. Show that G is solvable iff R = {1}. c.

• Well-Ordering and Division Theorem

  Use that argument and well-ordering to show that there can be no natural number a > 0 with b^2 = 2a^2 for some natural number b. 33. Let m be the least common multiple of a and b, and let c be a common multiple of a and b. Show that m divides c.

• subset

  In a Boolean ring R, show that a. 2x = 0 for all x  R. b. R is commutative. c. Every prime ideal P is maximal and R/P is a field with 2 elements. d. Every finitely generated ideal in R is principal. 3.

• Ring and fields

  241302 Rings and fields (a) If R is a field, show that R itself is a field of fractions for R. (b) Show that Q is a field of fractions for Z and for 2Z. please see attached pdf.

• Position Vector r(t) with Unit Vectors

  On an x,y axis system show r(0) and also r(3), then show vector D drawn from the head of r(0) to the head of r(3) showing that r(0) + D = r(3). b. From your drawing, find the magnitude and direction of the vector D. c.

• Fundamental Mathematics Sequences

  (1) * Show that the sequences ( 1/n) and (n + 1/2n) and Cauchy sequences, but the sequence (n) is not. (2) * Write down the definition of what it means for a sequence (an) to be convergent. Show that any convergent sequence is a Cauchy sequence.