Countable set

COT3103 10/21/2014 Exercises Section 2.5 2. Determine whether each of these sets is finite, countably infinite, or uncountable. For those that are countably infinite, exhibit a one-to-one correspondence between the set of positive integers and that set. a. The integers greater than 10. This is countably infinite. Starting from the first integer greater than 10, which is 11, one can infinitely count upwards since there is no boundary on the right side of the number line for this instance. The equation

Aristotle supported the idea of “potential infinity” but refuted the idea of “actual infinity”. He defined potential infinity by saying if you are counting natural numbers, logic would tell us that we can always add one to the previous number and that can potentially go on forever. He also said that we could potentially use this logic in geometry if we imagined a line that extended beyond both points with no recognizable end. On the contrary, actual infinity seems paradoxical because even if we had

defined by a finite set of natural numbers. This is almost ironic because part of his Pythagorean Theorem results in Pythagorean triplets,which includes numbers such as √2, which require an understanding of infinity in order to define (Rucker). On the other hand, Aristotle acknowledged that there existed concepts that point towards the existence of infinite, but that would contradict his defined and finite world. So, in order to handle these cases, he came up with the idea of labeling sets as “potentially

Finiteness has to do with the existence of boundaries. Intuitively, we feel that where there is a separation, a border, a threshold – there is bound to be at least one thing finite out of a minimum of two. This, of course, is not true. Two infinite things can share a boundary. Infinity does not imply symmetry, let alone isotropy. An entity can be infinite to its “left” – and bounded on its right. Moreover, finiteness can exist where no boundaries can. Take a sphere: it is finite, yet we can continue

1. What were your initial reactions to how this group is set up? How have your views changed at this point, if at all? I believe for me my initial reactions to how this group was set up is that everyone is in the same boat. By that I mean nobody (except for the professor) knew what to expect or what could happen. As I recall one of the initial conversations started at the beginning of the first class was about a complaint regarding smoking. This seemed to me a half hazard attempt at starting an easy

works, these standards put this into practice. A second groundbreaking document released by the National Council of Teachers Mathematics was Professional Standards for Teaching Mathematics. This set of standards “present[s] a vision of what teaching should entail to support the changes in curriculum set out in the Curriculum and Evaluation Standards. This document spells out what teachers need to know to teach toward new goals for mathematics education and how teaching should be evaluated for the

Religion had always been an important object in people’s lives for decades. Each religion had its own beliefs, rituals, and gods. In Ancient Egypt, there were multiple gods who control different places. Their religion also includes magic, mythology, and science. The people in Egypt believed life on Earth is only part of the eternal journey. They needed to live an earnest life on Earth and continue their journey in the afterlife. People in Egypt hinge on each other to complete their task and produce

Interaction points of spatial networks are linked to each other by what the writer’s term as channels, and they’re the paths through which material is transported. A definite sequence of linked edges in spatially embedded graph will form a channel. As you look at figure 1a, the roads are your channels, the pipeline network pipes, and tracks in railway networks are different examples of channels. The channels of which the writers have termed have exactly two end points, where the end points of a channel

.data s1: .asciiz "Enter first integer: " s2: .asciiz "Enter second integer: " s3: .asciiz "\nThe least common multiple of the two integers is: " .text .globl main main: li $v0, 4 la $a0, s1 syscall li $v0, 5 syscall move $a1,$v0 #puts integer 1 into $a1 li $v0, 4 la $a0, s2 syscall li $v0, 5 syscall move $a2, $v0 #puts integer 2 into $a2 #call for gcd addi $sp, $sp, -8 # makes the stack availible for 2 elements sw $a1, 4($sp) # stores integer 1 in $a1 sw $a2, 0($sp) jal

Tommy Adeosun ART2700 November 20, 2014 Mrs. King Isis Nursing Horus After learning so much about ancient Greece and many other ancient cultures from different parts of the world in class. In this essay I will analyze the artwork by giving a full 360 degree description of the work and every detail. I will also relate it to work we have studied in class. The work I will analyze is found at the Walters Art Museum, in Baltimore, Maryland. The title of the work is Isis Nursing Horus, an Egyptian artwork