real numbers, intervals, and inequalities
... they contain their endpoint, and intervals of the form (a, +⬁) and (−⬁, b) are considered to be open because they do not include their endpoint. The interval (−⬁, +⬁), which is the set of all real numbers, has no endpoints and can be regarded as both open and closed. This set is often denoted by the ...
... they contain their endpoint, and intervals of the form (a, +⬁) and (−⬁, b) are considered to be open because they do not include their endpoint. The interval (−⬁, +⬁), which is the set of all real numbers, has no endpoints and can be regarded as both open and closed. This set is often denoted by the ...
SD_AFNR_2011_Activity_12
... rational numbers as fractions. In the fraction a/b, a is the numerator and b is the denominator. Fractions can be smaller than 1, like ½, or larger than 1, like 5/2, which can be simplified to 2 ½. All integers can be thought of as rational numbers as well, with a denominator of 1, like 3 being writ ...
... rational numbers as fractions. In the fraction a/b, a is the numerator and b is the denominator. Fractions can be smaller than 1, like ½, or larger than 1, like 5/2, which can be simplified to 2 ½. All integers can be thought of as rational numbers as well, with a denominator of 1, like 3 being writ ...
The Pi-Phi Product
... odd integers. A sequence of partial sums involving only the odd integers and Fibonacci numbers can also be shown to yield the pi-phi product in the limit. The series was obtained from the Oberg formula which turns out to be a particular case of a broader class of problems dealing with the roots of a ...
... odd integers. A sequence of partial sums involving only the odd integers and Fibonacci numbers can also be shown to yield the pi-phi product in the limit. The series was obtained from the Oberg formula which turns out to be a particular case of a broader class of problems dealing with the roots of a ...
The Real Number Line 0.1 THE REAL NUMBER LINE AND ORDER
... positive and negative infinity. These symbols do not denote real numbers; they merely let you describe unbounded conditions more concisely. For instance, the interval b, is unbounded to the right because it includes all real numbers that are greater than or equal to b. ...
... positive and negative infinity. These symbols do not denote real numbers; they merely let you describe unbounded conditions more concisely. For instance, the interval b, is unbounded to the right because it includes all real numbers that are greater than or equal to b. ...
Detailed Lesson Plans
... Checking interactively, with Ps repeating aloud the points they have covered in the previous two lessons (operation of number machines, how to generate number sequences, prediction of differences of a sequence given its linear formula, finding the (e.g. 8th) term of a sequence if its formula is know ...
... Checking interactively, with Ps repeating aloud the points they have covered in the previous two lessons (operation of number machines, how to generate number sequences, prediction of differences of a sequence given its linear formula, finding the (e.g. 8th) term of a sequence if its formula is know ...
Letter to the Editor
... I'm afraid there was an error in the February issue of The Fibonacci Quarterly. Mr. Shallit's proof that phi is irrational is correct up to the point where he claims that 1/0 can't be an integer. He has no basis for making that claim, as 0 was defined as a rational number, not an integer. The proof ...
... I'm afraid there was an error in the February issue of The Fibonacci Quarterly. Mr. Shallit's proof that phi is irrational is correct up to the point where he claims that 1/0 can't be an integer. He has no basis for making that claim, as 0 was defined as a rational number, not an integer. The proof ...
