Whole Numbers
... ***can be expressed as a decimal that terminates or that repeats indefinitely. Ex. 0.125 or .81818181… 5. Irrational Numbers: a number that can NOT be written as a fraction in the form of a/b where a & b are integers and b does NOT = 0. ***can NOT be expressed as a terminating or repeating decimal! ...
... ***can be expressed as a decimal that terminates or that repeats indefinitely. Ex. 0.125 or .81818181… 5. Irrational Numbers: a number that can NOT be written as a fraction in the form of a/b where a & b are integers and b does NOT = 0. ***can NOT be expressed as a terminating or repeating decimal! ...
PDF
... setting: h1i hTheoremi h11A25i † This text is available under the Creative Commons Attribution/Share-Alike License 3.0. You can reuse this document or portions thereof only if you do so under terms that are compatible with the CC-BY-SA license. ...
... setting: h1i hTheoremi h11A25i † This text is available under the Creative Commons Attribution/Share-Alike License 3.0. You can reuse this document or portions thereof only if you do so under terms that are compatible with the CC-BY-SA license. ...
Here is the algorithm example for the week 8 discussion
... Example 2: (to be worked out in the discussion). Write and analyze a pseudocode algorithm that finds the product of the largest and smallest even integers in the list a 1, a2, …, an. The algorithm should return -1 (or some other negative value) if there are no even numbers. If there is just one even ...
... Example 2: (to be worked out in the discussion). Write and analyze a pseudocode algorithm that finds the product of the largest and smallest even integers in the list a 1, a2, …, an. The algorithm should return -1 (or some other negative value) if there are no even numbers. If there is just one even ...
Set-Builder Notation
... Verbally this reads: The set of all x such that x is greater than or equal to 8 and x is an element of the set of whole numbers ...
... Verbally this reads: The set of all x such that x is greater than or equal to 8 and x is an element of the set of whole numbers ...
1.1 Patterns and Inductive Reasoning
... What conjecture can you make about the sum of the first 100 even numbers? In other words, what rule are you following? ...
... What conjecture can you make about the sum of the first 100 even numbers? In other words, what rule are you following? ...
Unit 1: Value and Magnitude of Rational Numbers
... Base: the number in an expression or equation which is raised to a power or exponent Counting (natural) numbers: the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, …, n} – how you naturally count E: a symbol used in a calculator to indicate that the ...
... Base: the number in an expression or equation which is raised to a power or exponent Counting (natural) numbers: the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, …, n} – how you naturally count E: a symbol used in a calculator to indicate that the ...
Special Facts to Know
... Fibonacci – F0 = 0, F1 = 1, Fn = Fn-1 + Fn-2 for n > 1 Lucas – F0 = 2, F1 = 1, Fn = Fn-1 + Fn-2 for n > 1 Let s(n) be the sum of all the proper factors of n. Deficient – s(n) < n Perfect – s(n) = n Abundant – s(n) > n Let d(n) be the total number of digits in the prime factorization of n. Frugal / E ...
... Fibonacci – F0 = 0, F1 = 1, Fn = Fn-1 + Fn-2 for n > 1 Lucas – F0 = 2, F1 = 1, Fn = Fn-1 + Fn-2 for n > 1 Let s(n) be the sum of all the proper factors of n. Deficient – s(n) < n Perfect – s(n) = n Abundant – s(n) > n Let d(n) be the total number of digits in the prime factorization of n. Frugal / E ...
Name
... Closure Property – when you perform an operation on a set of numbers, that set is said to be closed under that operation if when you perform the operation on any numbers within that set, the result is a number within that set of numbers. o The set of whole numbers is said to be closed under addition ...
... Closure Property – when you perform an operation on a set of numbers, that set is said to be closed under that operation if when you perform the operation on any numbers within that set, the result is a number within that set of numbers. o The set of whole numbers is said to be closed under addition ...
Practice counting in tens from any number. E.g. 6, 16, 26, 36 Add
... tens from any number. E.g. 6, 16, 26, 36 ...
... tens from any number. E.g. 6, 16, 26, 36 ...
an equation that states two ratios are equal is called a proportion
... AN EQUATION THAT STATES TWO RATIOS ARE EQUAL IS CALLED A PROPORTION. THE NUMBERS A AND D ARE CALLED THE EXTREMES. NUMBERS B AND C ARE CALLED THE MEANS. TO SOLVE A PROPORTION YOU TAKE THE PRODUCT OF THE EXTREMES AND SET IT EQUAL TO THE PRODUCT OF THE MEANS. ...
... AN EQUATION THAT STATES TWO RATIOS ARE EQUAL IS CALLED A PROPORTION. THE NUMBERS A AND D ARE CALLED THE EXTREMES. NUMBERS B AND C ARE CALLED THE MEANS. TO SOLVE A PROPORTION YOU TAKE THE PRODUCT OF THE EXTREMES AND SET IT EQUAL TO THE PRODUCT OF THE MEANS. ...
CounterExamples (Worksheet)
... a. The sum of two odd numbers is even. b. The sum of two even numbers is even. c. The product of two odd numbers is even. d. The product of two even numbers is even. 2. Jim says ‘Prime numbers are always odd’. Prove that Jim is wrong. 3. ‘The square root of a number is always smaller than the number ...
... a. The sum of two odd numbers is even. b. The sum of two even numbers is even. c. The product of two odd numbers is even. d. The product of two even numbers is even. 2. Jim says ‘Prime numbers are always odd’. Prove that Jim is wrong. 3. ‘The square root of a number is always smaller than the number ...
PDF
... A k-superperfect number n is an integer such that σ k (n) = 2n, where σ k (x) is the iterated sum of divisors function. For example, 16 is 2-superperfect since its divisors add up to 31, and in turn the divisors of 31 add up to 32, which is twice 16. At first Suryanarayana only considered 2-superper ...
... A k-superperfect number n is an integer such that σ k (n) = 2n, where σ k (x) is the iterated sum of divisors function. For example, 16 is 2-superperfect since its divisors add up to 31, and in turn the divisors of 31 add up to 32, which is twice 16. At first Suryanarayana only considered 2-superper ...