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.