Inequality Proofs
... The statement is false. For example, 2 > 1 and −1 > −2, but 2 · (−1) 6> 1 · (−2). This result shows that you have to be careful in the rules you use to work with inequalities. Some “rules” which look obvious aren’t correct. ...
... The statement is false. For example, 2 > 1 and −1 > −2, but 2 · (−1) 6> 1 · (−2). This result shows that you have to be careful in the rules you use to work with inequalities. Some “rules” which look obvious aren’t correct. ...
Revised Version 070430
... for the summation of the first n natural numbers. As an alternate to directly dealing with the general case, consider two specific examples. There are two basic cases for the natural number n, namely n could be an even or an odd number. Suppose that n = 16. One way to add the numbers 1, 2, …, 16, is ...
... for the summation of the first n natural numbers. As an alternate to directly dealing with the general case, consider two specific examples. There are two basic cases for the natural number n, namely n could be an even or an odd number. Suppose that n = 16. One way to add the numbers 1, 2, …, 16, is ...
Full text
... Also, it is apparent that jf [ satisfying (1) implies that j - f j satisfies (1) and it is convenient to associate a sequence with its negative. ...
... Also, it is apparent that jf [ satisfying (1) implies that j - f j satisfies (1) and it is convenient to associate a sequence with its negative. ...
PCH (3.3)(2) Zeros of Polynomial 10
... If c > 0, and if all the numbers in the third row of the synthetic division are either positive or zero, the c is an upper bound for the real zeros of f(x). If c < 0, and if the numbers in the third row of the synthetic division are alternately positive and negative (0 is considered to be either pos ...
... If c > 0, and if all the numbers in the third row of the synthetic division are either positive or zero, the c is an upper bound for the real zeros of f(x). If c < 0, and if the numbers in the third row of the synthetic division are alternately positive and negative (0 is considered to be either pos ...