The mathematical notion of infinity can be conceptualized in many different ways. First, as counting by hundreds for the rest of our lives, an endless quantity. It can also be thought of as digging a whole in hell for eternity, negative infinity. The concept I will explore, however, is infinitely smaller quantities, through radioactive decay
Infinity is by definition an indefinitely large quantity. It is hard to grasp the magnitude of such an idea. When we examine infinity further by setting up one-to-one correspondence’s between sets we see a few peculiarities. There are as many natural numbers as even numbers. We also see there are as many natural numbers as multiples of two. This poses the problem of designating the cardinality of the natural numbers. The standard symbol for the cardinality of the natural numbers is o. The set of even natural numbers has the same number of members as the set of natural numbers. The both have the same cardinality o. By transfinite arithmetic we can see this exemplified.
1 2 3 4 5 6 7 8 …
0 2 4 6 8 10 12 14 16 …
When we add one number to the set of evens, in this case 0 it appears that the bottom set is larger, but when we shift the bottom set over our initial statement is true again.
1 2 3 4 5 6 7 8 9 …
0 2 4 6 8 10 12 14 16 …
We again have achieved a one-to-one correspondence with the top row, this proves that the cardinality of both is the same being o. This correspondence leads to the conclusion that o+1=o. When we add two infinite sets together, we also get the sum of infinity; o+o=o.
This being said we can try to find larger sets of infinity. Cantor was able to show that some infinite sets do have cardinality greater than o, given 1. We must compare the irrational numbers to the real numbers to achieve this result.
1 0.142678435
2 0.293758778
3 0.383902892
4 0.563856365
: :
No mater which matching system we devise we will always be able to come up with another irrational number that has not been listed. We need only to choose a digit different than the first digit of our first number. Our second digit needs only to be different than the second digit of the second number, this can continue infinitely. Our new number will always differ than one already on the list by one digit.
All things may be divided into one of four classes: Finite, Infinite, the union of the two, and the cause of the union.
n2 + 5n + n + 5 - n2 - 6n (n2 cancel out with - n2, 5n + n cancel out
He expands on this by explaining the notion that there is a divine, infinite being, such as God, that is innate. Among these statements, Descartes doubts everything he has ever been told in his life, and only keeps the belief that there is an infinite being out there. In Meditations, he explicitly states “Nevertheless I have long had fixed in my mind the belief that an all-powerful God existed by whom I have been created such as I am.”
Nathaniel Hawthorne uses the color red significantly throughout The Scarlet Letter to show its importance of symbolism in the emotions of sin and passion that it represents. The first example in The Scarlet Letter is the red rose that is growing by the prison door (2), which represents Hester’s pride and passion. This rose is growing in a place that is not very fitting, which is identical to Hester’s passion in that she does not fit into the Puritan society. Another example of how red is used to symbolize Hester’s passion occurs later when there is sunlight passing through a red window in the governor’s house, which in turn spreads red light throughout the room. This represents Hester’s passion as it spreads throughout the Puritan society. Also in The Scarlet Letter, Hawthorne uses the color red to symbolize Hester’s sin, which is continually being shown by the scarlet letter “A”. Hester’s sin through the scarlet letter is something that she has to continually deal with and that she can’t escape. Hester’s daughter Pearl, who is the product of Hester’s sin, is often seen to be dressed in red clothes and is also called names like “ Ruby”, “Red Rose”, and “Coral” by her mother (61). The symbolism of the color red in The Scarlet Letter is portrayed as the most important of all, as it is what the entire novel is based upon through the scarlet letter that Hester is forced to wear.
Over time, the modern family model has changed in a variety of ways; when it comes to families, the social norms are greatly different than they were only a couple decades back. With these changing times, it makes it harder for there to be a definite definition as to what a modern family truly entails. The following subtopics are all responsible for this changing modern family model:
"Because all created things are limited, that which comes before and after them must be boundless" (Gaarder, Jostein 34)
But as St. Thomas said some predicates may be said to add to being inasmuch as they express a mode of being not expressed by the term being4. Thus, there are three ways of addition. The first way of addition is when some reality outside the essence are added to a thing. For example, If Médard was not black, he would still be a man, for blackness is outside the essence of Médard.
It seems that there is no God. For if one of two contraries were infinite, the other would
Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:
Neale, Vicky. "Theorum11the pigeonhole principle." Theorem of the Week. Cambridge Maths Tripos, 25 March 2009. Web. 8 Dec 2013. .
Before 1990s, waterfall is a common software development but it has its own problems such as it assumes that all project requirements can be gathered at the beginning of the project. It like mission impossible, because during development process there are many outside and inside problem influences to the project such as customer want to change some of the product function or developer quit project. Therefore, agile software development is birth to improve problem from earlier software development.
Agile is an iterative based software development methodology. In this particular approach a certain functionality of the software is developed in two to four numbers. The client or the partner for whom the system or the software is being developed stays in constant communication throughout as their feedback forms the basis of the next iteration. Since the feedbacks are readily and easily available, the final outcome rarely turns out to be undesirable for the clients.
Consequentially, the Waterfall consists of seven procedural steps followed in linear order, but possess small gates where information, specifications, and designs are reviewed. The seven procedural steps performed by software companies, according to Lotz (2013): “1. Gather and document requirements, 2. Design, 3. Code and unit test, 4. Perform system testing, perform user acceptance testing (UAT), 6. Fix any issues, and 7. Deliver the finished product.” However, the Waterfall methodology clear and defined linear plan provides development teams distinct guidelines for each phase of development, but the methodology still possesses pros and cons for usage. The advantages of the methodology are discipline provided by the procedural phase structure, current phase of the development team easily identifiable by vendor and client, and provides efficient knowledge transfer between team members. (Melonfire, 2008) Furthermore, the associated disadvantages of the methodology are the phases are not flexible to change, developers cannot return to a previous phase, and originally develop designs are not feasible. Finally, the trait of not being flexible deems Waterfall appropriate for well-defined projects, and projects with a fixed-price, a fixed-timeline, and a none adjustable scope. (Base36,
Teachers’ principles shape their behaviour, interactions with students, and curricular decisions. I aim to become a teacher who can create an effective teaching by developing habits of mind. In order to do so, I would have to continuously reflect, observe, assess, and evaluate. Assessments for learning, as learning, and of learning are crucial when developing a deep learning. At the beginning of a year, I would see the baseline of where each student is at and observe his or her progress. Then, I would make students self-regulate by making goals and assessing with peers since teachers won’t always be with them throughout their lifetime. Finally, I would question myself if I did my job well enough and if they learnt the materials. Different learning styles of each student are needed to perform the diverse educational system. As well as applying these ideas to classroom practice, I would need to think about how multiculturalism enables different beliefs and value systems to co-exist, creating tolerance, diverse society. Every culture and their languages should be respected in order to help students to keep a part of who they are. In Canada and other parts of the Western World, schools are no longer simply academic environments; they are also social sites where identities and power relations are negotiated and renegotiated with language issues featuring very promptly in the process. My