What Math Critical Thinking Questions Ought to Have Looked Like

-D27, M09, Y14-
Hello all, great to (figuratively) see you all here again. So it has been a week, and I can legitimately say that, if any of you ever wondered if folding a strip of paper from end to end, and from left to right, had a pattern...it does.
If you are having trouble envisioning this, then I cannot help you--I attempted to use brackets, underscores, and the like to create a visual of the process, but even I could not comprehend such meaningless chicken scratch.
Aside from discovering a 'mirror image' of folds pointing upwards and folds pointing downwards with the same friend of mine (let us dub him 'Steve' for future reference), I also ended up determining a mathematical expression between the number of folds created by folding n number of times, and the number of folds pointing downwards:
((2^n) - 1) / (2^n-1)
Sure, that was not the point of the problem-solving exercise, but it is nonetheless amazing to discover  an expression for something that people would often be quick to deem as 'random.'

Over the past week, we learned about the logic symbols Conjunction, Disjunction, and Negation, as well as how some laws of arithmetic apply to these operations. Conjunctions equate with logical "and," Disjunctions equate with inclusive "or," and Negations clearly equate with "not." This may sound simplistic, but it is not. Combined with actual expressions, these operations explode into a mess of venn diagrams and truth tables in the hopes of translating math logic into an intelligible language. It still does not sound that bad, you say? Here is a link to De Morgan's law, which is a tautology that uses negation to alter conjunctions and disjunctions:
http://en.wikipedia.org/wiki/De_Morgan's_laws

Now that I look at it more closely, it is not as difficult an idea to ingest--you were right. In essence, De Morgan's first proposition asserts that nothing at all satisfies P's standards and Q's standards--or in other words, nothing at all in P or nothing at all in Q (or is inclusive).

Of course, all this logic engenders another question: how do mathematical expressions deal with language paradoxes?
An example:
The following sentence is True.
The previous sentence is False.

Maybe having a programming language deal with the paradox would be the best way to test a paradoxes' mathematical translation. At the moment, an infinite loop seems to be the most viable result.

Thank you for reading.

Expressing Logic: Vacuous Truths

-D20, M09, Y14-
Herzlich willkommen once again to the meager few who have discovered this on the internet or have been tasked with reading this. I know you are just as excited as I am for the latest installment of this diary blog post.

To follow up on my previous confusion concerning {x in S2 for x in S1}, I did not in fact ask the professor for an explanation of the usage of the word "for;" rather, I asked a friend of mine who is also taking the class, but is vastly more experienced in the realm of computer science in general. The use of the word "for" simply explains to the computer--and to the programmer--that the program will evaluate each element (x) that is in S2, and then compare it with the elements within S1. In my mind's eye, I perceive this as a scanning beam going over the various objects within a box labeled S2, and then the same beam scanning a box labeled S1 for the same objects or for objects that are clearly not the same. Not the most exciting analogy admittedly, but it makes sense to me.

Now, concerning vacuous truths. The logic is quite fantastic, for in beginning with a false premise/antecedent, it does not matter if the conclusion is true or false, because the statement is true. This is the summit of arrogance, and it is hilarious. I can legitimately say, that for all cakes that are within the known universe, the cake that can alter the gravitational field around it is also the cake that can harness thrust without a propulsion system.
Now you must find me a cake that satisfies my antecedent but does not satisfy my conclusion.
No matter how hard you try, no matter the sweat, tears, and blood, you will never produce a counterexample to my claim.

Which means I am right.
-Aside-
This is eerily similar to an event on tumblr spoken of as "the science side of tumblr."
An example: http://i.imgur.com/bTL2DNe.jpg
The antecedent is that the kitten with a hat on its body is a turtle. The conclusion is that the type of turtle it is, is dubbed "mitochondria."  Thus, it is true that all 'turtles' of that kind are mitochondria.

Thank you for reading. As in, you reading => my gratitude.

Report Upon Creation

-Day11, Month09, Year14-
I went ahead and created this blog early out of habit. Hello and Welcome to my retreat, where I will report on a weekly basis the trials and tribulations of CSC165. To the TAs and instructors, I offer a hearty welcome. To any fellow students who grace this website with their presence, I give my regards.

Because this blog is primarily for offering my experience of CSC165, I shall begin:
The first class of the course was welcoming and fairly straightforward: the course aims to develop the skill of communicating ideas, thoughts, and actions through a programming medium.
The second class threw a bit of a curve ball when Instructor Heap had us attempt to translate three python expressions into english. Honestly, when that paper was handed to me, and I looked at the expressions, I wanted to panic. However, with numerous references to the notes I had been taking on translating mathematical expressions into Python expressions, I slowly began to understand the relationship between the two sets in each question.
Unfortunately, by the time these relationships began forming coherent words and phrases in my mind, it was time to collect the papers.

This experience was somewhat intimidating, especially since a number of students (who appeared to be older than myself) were able to answer the questions in the same amount of time I had been given. I worked backwards from their answers to my ambiguous understanding, and then put the answer to the first question in my own words. This is what I focused on in question 0:
return not all ({x in S2 for x in S1})

Then, I replaced the letters within the curly brackets with mathematical symbols, which I cannot display since the inclusive symbol is not available on my keyboard, and wrote:
For all x elements in S1, the program will compare these to all x elements in S2, and return the x element(s) that satisfy "not all," which is equivalent to saying "any" element that is in S1 and not in S2.

I turned off the bold tool for the last part because I am not certain of how that conclusion is reached. Does the word "for" lead to this conclusion? I must not know how it is used in this context, so I will ask Professor Heap after class.

This class will be a challenge, but I'd prefer it if the challenge originated from dealing with hard questions and not from being unaccustomed to terminology.

Thank you for reading this report. I do not know if this is how long blog posts ought to be, but feel free to comment, question, and silently laugh or sigh about what I have said.
Cheers.