Notes
... • For example, if we have 36m of fencing and wish to create a square pen we can use an equation to help. • Remember the equation for the perimeter of a square is P = 4l. • If the perimeter is 36m, then 36 = 4l. • This gives a length of 9m for each side. ...
... • For example, if we have 36m of fencing and wish to create a square pen we can use an equation to help. • Remember the equation for the perimeter of a square is P = 4l. • If the perimeter is 36m, then 36 = 4l. • This gives a length of 9m for each side. ...
![[Part 2]](http://s1.studyres.com/store/data/008795711_1-6aefa4cb45dd9cf8363a901960a819fc-300x300.png)
Exam April 05, 2016
... A local maximum is a number which is greater than both its predecessor and its successor. For example if the method is called with the array {2,0,1,6,0,4,0,5} then it should return 3 since at index 3 is the number 6 where 6 > 1 and 6 > 0. The first number in the sequence doesn’t have a predecessor w ...
... A local maximum is a number which is greater than both its predecessor and its successor. For example if the method is called with the array {2,0,1,6,0,4,0,5} then it should return 3 since at index 3 is the number 6 where 6 > 1 and 6 > 0. The first number in the sequence doesn’t have a predecessor w ...
Lecture Notes for Section 8.1
... If a nonempty set S of real numbers has a lower bound, then it has a greatest lower bound. Equivalently, if S has an upper bound, then it has a least upper bound. Note that this is an axiom; it a statement we accept as being true without proof. Axioms form the foundation upon which all other theorem ...
... If a nonempty set S of real numbers has a lower bound, then it has a greatest lower bound. Equivalently, if S has an upper bound, then it has a least upper bound. Note that this is an axiom; it a statement we accept as being true without proof. Axioms form the foundation upon which all other theorem ...
Cauchy Sequences
... In any metric space S, a divergent Cauchy sequence, because it “converges to a hole,” detects a hole into which S could fit another point. A metric space that has no such holes is called a complete metric space: Definition 4 A metric space S is complete iff every Cauchy sequence in S has a limit in ...
... In any metric space S, a divergent Cauchy sequence, because it “converges to a hole,” detects a hole into which S could fit another point. A metric space that has no such holes is called a complete metric space: Definition 4 A metric space S is complete iff every Cauchy sequence in S has a limit in ...
A) An arithmetic sequence is represented by the explicit formula A(n)
... Continued… Objectives: ...
... Continued… Objectives: ...
Solutions to problem sheet 1.
... filling-in the blanks in 2, 3, 6, , , 9, . . . is if a4 = 7 and a5 = 8. Using rule (ii) again we get a7 = aa4 = 12 and a8 = aa5 = 15 and a9 = aa6 = 18. (c) One can continue to argue like this indefinitely, using rule (ii) to deduce some terms further down the sequence and then finding that there i ...
... filling-in the blanks in 2, 3, 6, , , 9, . . . is if a4 = 7 and a5 = 8. Using rule (ii) again we get a7 = aa4 = 12 and a8 = aa5 = 15 and a9 = aa6 = 18. (c) One can continue to argue like this indefinitely, using rule (ii) to deduce some terms further down the sequence and then finding that there i ...
Sequence
In mathematics, a sequence is an ordered collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. Formally, a sequence can be defined as a function whose domain is a countable totally ordered set, such as the natural numbers.For example, (M, A, R, Y) is a sequence of letters with the letter 'M' first and 'Y' last. This sequence differs from (A, R, M, Y). Also, the sequence (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence. Sequences can be finite, as in these examples, or infinite, such as the sequence of all even positive integers (2, 4, 6,...). In computing and computer science, finite sequences are sometimes called strings, words or lists, the different names commonly corresponding to different ways to represent them into computer memory; infinite sequences are also called streams. The empty sequence ( ) is included in most notions of sequence, but may be excluded depending on the context.