THE REGIONS OF A CIRCLE - National Association of Math Circles
... Using this data, one can pose the following question: “Can anyone make a conjecture about the number of regions for n = 6 or for any n?” It is natural to expect that someone will propose that for any n, the number of regions created by the lines joining n pairs of dots will be 2n−1 . But could this ...
... Using this data, one can pose the following question: “Can anyone make a conjecture about the number of regions for n = 6 or for any n?” It is natural to expect that someone will propose that for any n, the number of regions created by the lines joining n pairs of dots will be 2n−1 . But could this ...
GETE0101
... incorrect. For which race is the conclusion most suspect? For what reason? 48. Communications The table shows the GPS number of commercial radio stations in the United States for a 50-year period. See a. Make a line graph of the data. back of book. b. Use the graph and inductive reasoning to make a ...
... incorrect. For which race is the conclusion most suspect? For what reason? 48. Communications The table shows the GPS number of commercial radio stations in the United States for a 50-year period. See a. Make a line graph of the data. back of book. b. Use the graph and inductive reasoning to make a ...
Series - hrsbstaff.ednet.ns.ca
... series of numbers, which have something in common with one another. In a sequence, there are term values and term numbers. The term values are the numbers, which are part of the sequence, which have something in common with one another. The term numbers are just the numbers in the order of each term ...
... series of numbers, which have something in common with one another. In a sequence, there are term values and term numbers. The term values are the numbers, which are part of the sequence, which have something in common with one another. The term numbers are just the numbers in the order of each term ...
Sum-free sets. DEFINITION 1: A subset A of an abelian group (G,+)
... Sum-free sets. D EFINITION 1: A subset A of an abelian group (G, +) is said to be sum-free if A ∩ (A + A) = φ, in other words, if there are no solutions in A to the equation x = y + z. The abelian groups which are of most interest to number theorists are Z and the groups Zp , where p is a prime. E X ...
... Sum-free sets. D EFINITION 1: A subset A of an abelian group (G, +) is said to be sum-free if A ∩ (A + A) = φ, in other words, if there are no solutions in A to the equation x = y + z. The abelian groups which are of most interest to number theorists are Z and the groups Zp , where p is a prime. E X ...
There are no Coincidences
... recursively. The merging requires n − 1 comparisons, where n is the total number of elements in both lists. Lemma 10. The parity of A003071(n) is 1 − m(n + 1). Proof. Let us first count the parity of comparisons for the powers of 2: n = 2k . When the number of lists is divisible by 4 then merging pa ...
... recursively. The merging requires n − 1 comparisons, where n is the total number of elements in both lists. Lemma 10. The parity of A003071(n) is 1 − m(n + 1). Proof. Let us first count the parity of comparisons for the powers of 2: n = 2k . When the number of lists is divisible by 4 then merging pa ...
Describe the pattern in the sequence and identify
... Vocabulary Geometric sequence Each term is found by multiplying the previous term by the same number ...
... Vocabulary Geometric sequence Each term is found by multiplying the previous term by the same number ...
Introduction to HyperReals
... Since b is finite there are real numbers s and t with s < b < t. Let A = { x | x is real and x < b }. A is non-empty since it contains s and is bounded above by t. Thus there is a real number r which is the least upper bound of A. We claim r b. Suppose not. Thus r b and Hence r-b is positive or ...
... Since b is finite there are real numbers s and t with s < b < t. Let A = { x | x is real and x < b }. A is non-empty since it contains s and is bounded above by t. Thus there is a real number r which is the least upper bound of A. We claim r b. Suppose not. Thus r b and Hence r-b is positive or ...
The Uniform Continuity of Functions on Normed Linear Spaces
... are points of S, and Y is a subset of S. Let us consider X, S, T and let us consider f . We say that f is uniformly continuous on X if and only if the conditions (Def. 1) are satisfied. (Def. 1)(i) X ⊆ dom f, and (ii) for every r such that 0 < r there exists s such that 0 < s and for all x1 , x2 suc ...
... are points of S, and Y is a subset of S. Let us consider X, S, T and let us consider f . We say that f is uniformly continuous on X if and only if the conditions (Def. 1) are satisfied. (Def. 1)(i) X ⊆ dom f, and (ii) for every r such that 0 < r there exists s such that 0 < s and for all x1 , x2 suc ...
BIG IDEA #2 - matermiddlehigh.org
... Identify zeros and their multiplicities. Understand and use the Intermediate Value Theorem on a function over a closed interval. Understand the relationship between degree and turning points. Graph polynomial functions with and without technology. Use long division to divide polynomials. Use synthet ...
... Identify zeros and their multiplicities. Understand and use the Intermediate Value Theorem on a function over a closed interval. Understand the relationship between degree and turning points. Graph polynomial functions with and without technology. Use long division to divide polynomials. Use synthet ...
