Chapter Excerpt
... Real numbers are denoted by ℝ and are numbers that can be shown by an infinite decimal representation such as 3.286275347.... The real numbers include rational numbers such as 42 and −23/129, and irrational numbers, such as the 2 and π, which can be represented as points along an infinite number lin ...
... Real numbers are denoted by ℝ and are numbers that can be shown by an infinite decimal representation such as 3.286275347.... The real numbers include rational numbers such as 42 and −23/129, and irrational numbers, such as the 2 and π, which can be represented as points along an infinite number lin ...
complex numbers - SCIE Mathematics
... We can write any complex number in this form re i As before, r is the modulus and θ is the argument. ...
... We can write any complex number in this form re i As before, r is the modulus and θ is the argument. ...
Regular and Semiregular Polyhedra
... Since the result must be positive, we conclude that (k − 2)(r − 2) must be less than 4. Of course, k and r must each be at least 3. So the choices for (k − 2) and (r − 2) are: k−2 r−2 ...
... Since the result must be positive, we conclude that (k − 2)(r − 2) must be less than 4. Of course, k and r must each be at least 3. So the choices for (k − 2) and (r − 2) are: k−2 r−2 ...
Properties of numbers Year 2 Summer 12
... – The digits add up to 11. • Guess a number less than 50 by asking questions about its properties to which only ‘Yes’ or ‘No’ answers are given, e.g. ...
... – The digits add up to 11. • Guess a number less than 50 by asking questions about its properties to which only ‘Yes’ or ‘No’ answers are given, e.g. ...
1. 1/(1 − 1 ) = 2. Dick is 6 years older than Jane. Six years ago he
... 6. 4. [34,42] Either x2 − 25x + 144 = 0 or x2 + 25x + 144 = 0. The first has solutions 9 and 16, while the second has solutions −9 and −16. 7. 71. [22,38] We must have y = 2z and then x + 7z = 500. Now z can equal any number from 1 to 71, and x will be uniquely determined. 8. 25. [34,65.5] If ` deno ...
... 6. 4. [34,42] Either x2 − 25x + 144 = 0 or x2 + 25x + 144 = 0. The first has solutions 9 and 16, while the second has solutions −9 and −16. 7. 71. [22,38] We must have y = 2z and then x + 7z = 500. Now z can equal any number from 1 to 71, and x will be uniquely determined. 8. 25. [34,65.5] If ` deno ...
Full text
... We let Fn represent the nth Fibonacci number. In [2] and [3] we find relationships between the Fibonacci numbers and their associated matrices. The purpose of this paper is to develop relationships between the generalized Fibonacci numbers and the permanent of a (0,1)-matrix. The kgeneralizedFibonac ...
... We let Fn represent the nth Fibonacci number. In [2] and [3] we find relationships between the Fibonacci numbers and their associated matrices. The purpose of this paper is to develop relationships between the generalized Fibonacci numbers and the permanent of a (0,1)-matrix. The kgeneralizedFibonac ...
Prime Time 1.5
... relationships among sets of objects that have certain attributes. • This means a Venn Diagram shows what groups have in common and what they don’t! ...
... relationships among sets of objects that have certain attributes. • This means a Venn Diagram shows what groups have in common and what they don’t! ...
The Natural Number System: Induction and Counting
... Claim 2. [0, ∞) is inductive. Let x ∈ [0, ∞). Then, by definition of the interval [0, ∞), x ≥ 0. By Axiom 6 of the real number system (and the defining property of 0), x + 1 ≥ 1. We proved earlier that 1 > 0. So by transitivity, x + 1 > 0. Thus, we have shown that [0, ∞) is inductive: if x ∈ [0, ∞), ...
... Claim 2. [0, ∞) is inductive. Let x ∈ [0, ∞). Then, by definition of the interval [0, ∞), x ≥ 0. By Axiom 6 of the real number system (and the defining property of 0), x + 1 ≥ 1. We proved earlier that 1 > 0. So by transitivity, x + 1 > 0. Thus, we have shown that [0, ∞) is inductive: if x ∈ [0, ∞), ...