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... November 1980) It Is well known that the sequence of the (natural) logarithms reduced mod 1 of the terms Fm of the Fibonacci sequence are dense in the unit interval. See [1], [2]. This is also the case when the logarithms are taken with respect to a base b, where b is a positive integer _> 2. In ord ...
... November 1980) It Is well known that the sequence of the (natural) logarithms reduced mod 1 of the terms Fm of the Fibonacci sequence are dense in the unit interval. See [1], [2]. This is also the case when the logarithms are taken with respect to a base b, where b is a positive integer _> 2. In ord ...
Exam 2 review sheet
... expansion that never terminates and is not periodic (doesn’t eventually repeat.) A rational number’s decimal expansion will either terminate or become eventually periodic. Given a terminating or periodic decimal expansion, be able to write it as a fraction. (i.e. write 12.34509090909… as a fractio ...
... expansion that never terminates and is not periodic (doesn’t eventually repeat.) A rational number’s decimal expansion will either terminate or become eventually periodic. Given a terminating or periodic decimal expansion, be able to write it as a fraction. (i.e. write 12.34509090909… as a fractio ...
Real Number System a.
... counterexample. “All negative numbers are integers.” False, because a negative number can be a fraction such as ½, which is not an integer. ...
... counterexample. “All negative numbers are integers.” False, because a negative number can be a fraction such as ½, which is not an integer. ...
What`s Rational and What`s Irrational ? Finding Square Roots of
... is between. 2. Divide - divide your number by one of those square roots. 3. Average - take the average of the result of step 2 and the root. 4. Use the result of step 3 to repeat steps 2 and 3 until you have a number that is accurate enough for you. Example: Find the square root of 10 ( ...
... is between. 2. Divide - divide your number by one of those square roots. 3. Average - take the average of the result of step 2 and the root. 4. Use the result of step 3 to repeat steps 2 and 3 until you have a number that is accurate enough for you. Example: Find the square root of 10 ( ...
Math Review
... • But it is also not divisible by any of the listed primes, contradicting the factorization of integers into primes. • We reach a contradiction ...
... • But it is also not divisible by any of the listed primes, contradicting the factorization of integers into primes. • We reach a contradiction ...
Chapter 1.1—Introduction to Integers Chapter 1.1-
... Two numbers are called "opposites" if one number is the same as another except that they have differing signs. I personally dislike the term opposite when used to describe numbers and will not use it very often. The "absolute value" of a number is its positive distance from the origin 0 . |−5| 5 a ...
... Two numbers are called "opposites" if one number is the same as another except that they have differing signs. I personally dislike the term opposite when used to describe numbers and will not use it very often. The "absolute value" of a number is its positive distance from the origin 0 . |−5| 5 a ...
Introduction to Algebraic Proof
... This section is a brief introduction to on how to prove mathematical conjectures using algebra. The following methods are the ones normally encountered at GCSE : ...
... This section is a brief introduction to on how to prove mathematical conjectures using algebra. The following methods are the ones normally encountered at GCSE : ...
Caitlin works part-time at the mall
... 7. Does -5 1/5 belong to each of the following sets? A Whole numbers Yes No B Integers Yes No C Rational numbers Yes No D Real numbers Yes No 8. Which statement shows that the set of irrational numbers is not closed under multiplication? (Circle correct answer) A 8 x 14 = 112 C. π ∙ 1 = π B √3 x 2 = ...
... 7. Does -5 1/5 belong to each of the following sets? A Whole numbers Yes No B Integers Yes No C Rational numbers Yes No D Real numbers Yes No 8. Which statement shows that the set of irrational numbers is not closed under multiplication? (Circle correct answer) A 8 x 14 = 112 C. π ∙ 1 = π B √3 x 2 = ...
Section 3.2: Sequences and Summations
... Def: A sequence is a function from a subset of the set of integers (usually the set of natural numbers) to a set S. We use the notation ak to denote the image of the integer k. Ex: Consider the sequence 1, 2, 3, 4, 5, 6, … We could specify this sequence as {ak} where ak = k + 1 and the sequence is ...
... Def: A sequence is a function from a subset of the set of integers (usually the set of natural numbers) to a set S. We use the notation ak to denote the image of the integer k. Ex: Consider the sequence 1, 2, 3, 4, 5, 6, … We could specify this sequence as {ak} where ak = k + 1 and the sequence is ...
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... of n independent random variables X^ (1 < i < n) identically and uniformly distributed on [0, 1]. Thus, we may reinterpret (2.1) to read: For 1 < k < n, Probffe - 1 < £ Xt < k J = Ank /nl ...
... of n independent random variables X^ (1 < i < n) identically and uniformly distributed on [0, 1]. Thus, we may reinterpret (2.1) to read: For 1 < k < n, Probffe - 1 < £ Xt < k J = Ank /nl ...
