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nature of mathematics

Questions and Answers of Nature Of Mathematics

In Chapter 1, we introduced Pascal’s triangle. The reproduction here is from a 14th-century Chinese manuscript, and in this form is sometimes called Yang Hui’s triangle. Even though we have not
The Ionic Greek numeration system (approximately 3000 b.c.) counts as follows: , , , , , F, s, , , , , , , , , " F, , , , , , Other numbers are A (for 30), (for 40), v (for 50), K (for 90), p (for
Is the set A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} closed for addition?
Is the set B = {0, 1} closed for multiplication?
Suppose you are selling tickets for a raffle, and the tickets cost $2 each. You sell 3 tickets on Monday and 4 tickets on Tuesday. How much money did you collect?
Explain each of the words or concepts in Problems 1–8.Multiplication
Explain each of the words or concepts in Problems 1–8.Subtraction
Explain each of the words or concepts in Problems 1–8.Closure for addition
Explain each of the words or concepts in Problems 1–8.Closure for multiplication
Explain each of the words or concepts in Problems 1–8.Commutativity
Explain each of the words or concepts in Problems 1–8.Associativity
Explain each of the words or concepts in Problems 1–8.Distributivity
Explain each of the words or concepts in Problems 1–8.Contrast commutativity and associativity.
Use the definition of multiplication to show what each expression in Problems 9–14 means.a. 2 · 3b. 3 · 2
Use the definition of multiplication to show what each expression in Problems 9–14 means.a. 3 · 4b. 4 · 3
Use the definition of multiplication to show what each expression in Problems 9–14 means.a. 5 · 2b. 2 · 5
Use the definition of multiplication to show what each expression in Problems 9–14 means.a. 2 · 184b. 184 · 2
Use the definition of multiplication to show what each expression in Problems 9–14 means.a. 3 · 145b. 145 · 3
Use the definition of multiplication to show what each expression in Problems 9–14 means.a. xyb. yx
In Problems 15–26, classify each as an example of the commutative property, the associative property, or both. E + S=S+ E
In Problems 15–26, classify each as an example of the commutative property, the associative property, or both. 2 + 3 + 5 = 2 + 5+ 3
In Problems 15–26, classify each as an example of the commutative property, the associative property, or both. 2+(3+5) = (2+ 3) + 5
In Problems 15–26, classify each as an example of the commutative property, the associative property, or both. 6+(2+3)= (6 + 2) + 3
In Problems 15–26, classify each as an example of the commutative property, the associative property, or both. 6+(2+3)= (6 + 3) + 2
In Problems 15–26, classify each as an example of the commutative property, the associative property, or both. (z + E) + 9 = ( + 7) +9
In Problems 15–26, classify each as an example of the commutative property, the associative property, or both. 6+(2+3)= (2+ 3) + 6
In Problems 15–26, classify each as an example of the commutative property, the associative property, or both. (9 + 6)(s + +) = (6 + 9)( + +)
In Problems 15–26, classify each as an example of the commutative property, the associative property, or both. (s + +)(6 + 9) = (6 + 9)( + +)
In Problems 15–26, classify each as an example of the commutative property, the associative property, or both. (3+5) + (2 + 4) =(3+5) + (4 + 2)
In Problems 15–26, classify each as an example of the commutative property, the associative property, or both. (s + c) + (+ + 2) = (t + 2) + (S+ )
In Problems 15–26, classify each as an example of the commutative property, the associative property, or both. (Z + S) + (t + c) = (t + 7) + (S + E)
“Isn’t this one just too sweet, dear?” asked the wife as she tried on a beautiful diamond ring. “No,” the husband replied.“It’s just too dear, sweet.” Does this story remind you of
Is the operation of putting on your shoes and socks commutative?
In the English language, the meanings of certain phrases can be very different depending on the association of the words.For example, (MAN EATING) TIGER is not the same as MAN (EATING TIGER)Decide
Think of three nonassociative word triples as shown in Problem 29.Data from Problem 29In the English language, the meanings of certain phrases can be very different depending on the association of
Why do you think addition of natural numbers was left undefined? Try to write a definition. Look in one or more dictionaries. What problems do you find with these definitions?
Is subtraction commutative in the set of counting numbers?
Consider the set A = {1, 4, 7, 9} with an operation ⊗ defined by the table. 1 4 7 9 1 9 7 1 4 4 7 9 4 1 7 1 4 7 9 9 4 1 9 7 ab means find the entry in row a and column b; for example, 79=9 (the
Consider the set with an operation 1 -1 1 -1 X 1 -1 F (1,-1, i, -i} = X defined by the table. i-i i -i 1 -i -1 i -i-1 1 -i i 1-1 a x b means find the entry in row a and column b; for example, -1
Consider the set A and the operation ⊗ from Problem 33. Is the set A closed for the operation of ⊗? Give reasons for your answer.Data from Problem 33Consider the set A = {1, 4, 7, 9} with an
Consider the set F and the operation of × from Problem 34. Is the set F closed for the operation of × ? Give reasons for your answer.Data from Problem 34Consider the set with an operation 1 -1 1
Consider the set A and the operation ⊗ from Problem 33.Does the set A satisfy the given property for the operation of ⊗? Give reasons for your answer.a. Associativeb. CommutativeData from
Consider the set F and the operation of × from Problem 34.Does the set F satisfy the given property for the operation of ×? Give reasons.a. Associativeb. CommutativeData from Problem 34Consider
Let a be the process of putting on a shirt; let b be the process of putting on a pair of socks; and let c be the process of putting on a pair of shoes. Let be the operation of “followed by.”
Let t be the process of brushing your teeth, h the process of washing your hair, and d the process of drying your hair. Let be the operation of “followed by.”
Tell whether each of the following is true or false, and give the meaning of each.a. 7 | 63b. 8 | 104c. 14 | 2d. 6 | 15
If x | (a + b) and x | a, then x | b.
Find a rule for the divisibility of any number M by 2.
Find a rule for divisibility by 3.
Find the prime factorizations:a. 385b. 1,400
Find the canonical representation of 3,465.
Find the greatest common factor of the given sets of numbers.a. 300, 144b. 15, 28c. 3,150, 588, 280
Find the least common multiple of 300, 144, and 108.
Show that there is no largest prime.
Explain the difference between number and numeral. Give examples of each.
Discuss the similarities and differences between a simple grouping system and a positional system. Give examples of each.
What do you regard as the shortcomings and contributions of the Egyptian numeration system?
What do you regard as the shortcomings and contributions of the Roman numeration system?
What do you regard as the shortcomings and contributions of the Babylonian numeration system?
Discuss addition and subtraction for Babylonian numerals. Show examples.
Tell which of the named properties apply to the Egyptian, Roman, and Babylonian numeration systems.a. Grouping systemb. Positional systemc. Repetitive system
Tell which of the named properties apply to the Egyptian, Roman, and Babylonian numeration systems.a. Additive systemb. Subtractive systemc. Multiplicative system
Write each numeral in Problems 9–20 as a decimal numeral. By decimal numeral, we mean the system we use in everyday arithmetic. . 66 UUU b. 99
Write each numeral in Problems 9–20 as a decimal numeral. By decimal numeral, we mean the system we use in everyday arithmetic. a. b. n
Write each numeral in Problems 9–20 as a decimal numeral. By decimal numeral, we mean the system we use in everyday arithmetic. 50 q ||| UU B
Write each numeral in Problems 9–20 as a decimal numeral. By decimal numeral, we mean the system we use in everyday arithmetic. a. On b. Do
Write each numeral in Problems 9–20 as a decimal numeral. By decimal numeral, we mean the system we use in everyday arithmetic. . a. 8 9 99 R2 6 || b. &
Write each numeral in Problems 9–20 as a decimal numeral. By decimal numeral, we mean the system we use in everyday arithmetic. a. XLVIII b. DCCIX
Write each numeral in Problems 9–20 as a decimal numeral. By decimal numeral, we mean the system we use in everyday arithmetic. a. DL b. CD
Write each numeral in Problems 9–20 as a decimal numeral. By decimal numeral, we mean the system we use in everyday arithmetic. a. VMMDC b. IXDCCXII
Write each numeral in Problems 9–20 as a decimal numeral. By decimal numeral, we mean the system we use in everyday arithmetic. a. YYYYY b. YYYY J
Write each numeral in Problems 9–20 as a decimal numeral. By decimal numeral, we mean the system we use in everyday arithmetic. a. Y d b. Y
Write each numeral in Problems 9–20 as a decimal numeral. By decimal numeral, we mean the system we use in everyday arithmetic. a. b. l
Write each numeral in Problems 9–20 as a decimal numeral. By decimal numeral, we mean the system we use in everyday arithmetic. a. dd DD b. J
Kathy had a dream in which she was selling roses in an international market. She started out with 143 roses. Then her first customer, an Egyptian, bought of them. Soon afterward, a Babylonian asked
In a strange mix-up, several people (no two of whom spoke the same language) needed to pool their resources to survive the scorching desert heat. Eric had 45 bottles of water; Dimetrius had
The Rhind papyrus contains many problems. Two are symbolized on the following simulated papyri. The one in Problem 24 is an 18th-century Mother Goose rhyme. Answer the question posed in each problem.
The Rhind papyrus contains many problems. Two are symbolized on the following simulated papyri. The one in Problem 24 is an 18th-century Mother Goose rhyme. Answer the question posed in each problem.
Write each of the numerals in Problems 25–30 in the Egyptian numeration system.47
Write each of the numerals in Problems 25–30 in the Egyptian numeration system.75
Write each of the numerals in Problems 25–30 in the Egyptian numeration system.258
Write each of the numerals in Problems 25–30 in the Egyptian numeration system.521
Write each of the numerals in Problems 25–30 in the Egyptian numeration system.852
Write each of the numerals in Problems 25–30 in the Egyptian numeration system.2,014
Write each of the numerals in Problems 31–36 in the Roman numeration system.47
Write each of the numerals in Problems 31–36 in the Roman numeration system.75
Write each of the numerals in Problems 31–36 in the Roman numeration system.258
Write each of the numerals in Problems 31–36 in the Roman numeration system.521
Write each of the numerals in Problems 31–36 in the Roman numeration system.852
Write each of the numerals in Problems 31–36 in the Roman numeration system.2,014
Write each of the numerals in Problems 37–42 in the Babylonian numeration system.47
Write each of the numerals in Problems 37–42 in the Babylonian numeration system.75
Write each of the numerals in Problems 37–42 in the Babylonian numeration system.258
Write each of the numerals in Problems 37–42 in the Babylonian numeration system.521
Write each of the numerals in Problems 37–42 in the Babylonian numeration system.852
Write each of the numerals in Problems 37–42 in the Babylonian numeration system.2,014
Perform the indicated operations in Problems 43–48. UUUU 66 + D2
Perform the indicated operations in Problems 43–48. TU U- IU RSS
Perform the indicated operations in Problems 43–48. ||| UUUU UUUU ||UU 66
Perform the indicated operations in Problems 43–48. ARRA +

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