Real Analysis

Let y1=1,and for each n belong to N define y_n+1=(3y_n+4)/4. >a-Use induction to prove that the sequence satisfies y_n<4for all n >belong to N. >b-use another induction argument to show the sequence(y1,y2,y3,...)is >increasing.

Real Analysis

"let A be boundd below and define B={b belong to R : b is lower bound for A}.show that sup B= inf A.

Real Analysis

if sup A < sup B then show that there exists an element b belong to B that is upper bound for A.

Probabilities

Question 1 A restaurant can serve up to 75 meals. Experience shows that 20% of clients who have booked do not turn up. 1. The manager accepts 90 bookings. What is the probability that more than 50 clients turn up? 2. How many bookings should the manager accept in order to have a probability of more than 0.9 that he will s ...continues

word problem

one-half of Heather's age two years from now plus one-third of her age three years ago is twenty years. How old is she now?

real analysis

assume that A And B are nonempty, bounded above and satisfy B subset or equal of A. Show that sup B<= sup A

Real analysis

let A subset or equal of R be bounded above and let c belong to R.Define the sets c+A and cA by c+A={c+a : a belong to A} and cA={ca : a belong to A}. 1-show that sup(c+A)=c+ Sup A 2-if c>=0,show that sup(cA)=cSupA 3-postulate a similar type of statement for sup(cA)for the case c<0

Real analysis

Prove that if a is an upper bound for A and if a is also an element of A, then it must be that a=sup A

square root theory proof

Pove that : 1)A real number y <0 has no square root. 2)he number y= 0 has exactly one square root , namely 0. 3)A real number y>0 has exactly two square roots, one positive and one negative. Proof: 1) Proof by contradiction when y<0 , assume that y has a square root . Then number x is called square root of y if x^2 ...continues

Real Analysis

Proof: Given any two real numbers a