Integers

If a and b are integers, show that ab = 0 if and only if a = 0 or b = 0 Exercise 1.

Show there is no interger a such that 2a = 1.

Show there is no interger a such that 2a = 1. Exercise 2.

Integer multiplication

Show that for integers a and b, ab = 1 if and only if a = b = 1 or a=b=-1.

Show that if a, b, c are intergers such that ac < bc and c > 0, then a < b.

Show that if a, b, c are intergers such that ac < bc and c > 0, then a < b. exercise 4.

Integer multiplication

show that if a,b are integers such that ac < bc and c < 0 then, a > b exercise 5.

Accounting for Merchandising Organizations

Les Fleurs, a boutique in Paris, France, had the following accounts in its accounting records at December 31, 20X2 (amounts in Euros, denoted as "E") Purchases………………... E250,000 Freight In……………… E8,000 Sales discounts…………. 4,000 Purchase returns…….. 7,000 Inventory Sales…………………. 400,000 December 31, 20X1….. 20 ...continues

Limit theorems

show that the following limits do not exist: use def. of convergence or cauchy or epsilon delta a. lim as x goes to 0 of (1/(x^2)) x>0 b. lim as x goes to 0 of (1/(x^1/2)) same as (1/sqrtx) c. lim as x goes to 0 of (x + sgn(x)) d. lim as x goes to 0 of sin(1/(x^2)) let f: R---> R be defined by setting f(x)= x if x is ...continues

Riemann integral

define f(x) = x if x is rational and f(x)=0 if x is irrational. Compute the integration 1top0bottom f dx and integration 1top0bottom f dx. is f integrable on [0,1]? the first integration is upper sums and the second is lower sums

Mean value theorem

use the MVT to prove that ny^(n-1)(x-y)greater than or equal to x^n-y^n greater than or equal to nx^(n-1)(x-y if n less than or equal to 1 and 0 less than or equal to y less than or equal to x

For any integer a, argue that a + 3 > a + 2

1)For any integer a, argue that a + 3 > a + 2 3) An integer a is divisible by an integer b means there is an integer z such that a = b x z. use any properties of the integers through page 14 to prove that fir integers a,b and c such that if a is divisible by b and b is divisible by c the a is divisible by c. 4) let Z deno ...continues