Positive integer proof

Prove that the product of two positive integers is a positive integer using the 5.4 Some new notations of the attached document

Negative integer product

prove that the product of two negative integers is a positive integer using the 5.4 Some new notations of the attached document

Positive and negative product

prove that the product of a negative integer and a positive integer is a negative integer using the 5.4 Some new notations of the attached document

Natural numbers

Suppose the sum of two natural numbers a,b is the natural number c. Prove that (+a)+(+b)= +c using the 5.4 Some new notations of the attached document

Natural numbers

Suppose the sum of two natural numbers a,b is the natural number c. Prove that (+a)(+b)= +c using the 5.4 Some new notations of the attached document

Argue that m x m not equal to m + m.

Here is what I have can you add anything to help this out? You want to show that if m is a natural number (0, 1, 2, 3, ...), then m x m is not equal to m + m. You can do this simply by showing that it is not in at least one case (because if it's not true for at least one natural number, then it's not true for natural numbers ...continues

limit theorems and series

By using partial fractions show that a. the sumation from 0 to infinity of 1/(n+1)(n+2)=1 b. the sumation from 0 to infinity of 1/(alpha+n)(alpha+n+1)=1/alpha >0 if alpha>0 c. the sumation from 0 to infinity of 1/n(n+1)(n+2) =1/4 apply the theorem: let (Xsubn) be a sequence of positive real numbers such that L := lim(Xsubn ...continues

Limits

a. Let f: R--->R and let c be element in R. Show that the lim from x to c of f(x)=L if and only if lim from x to 0 of f(x+c)=L (if and only if: go both ways) b. Use either the epsilon-delta definition (which states: Let A be a subset of the reals and let c be a cluster point of A. For a function f: A--->R, a real number L is ...continues

Midpoint Rule and Composite Integral Approximation

see attached. Derive the composite rule...based on the midpoint rule...

Approximating derivatives

see attached. Derive the following two formulas for approximating derivatives and show that they are both O(h^4) by establishing their error terms.