all the prerequisites for writing a proof!

After we learned how to tell things in a totally new language ( the logical language), we started to learn its properties: conjunctions, disjunctions, negations. The fundamental connection between con/disjunction is mentioned in the last slog, which is, "not p or q" = "p implies q". It is indeed a very fascinating concept. Using this property, I deduced the reason why the contrapositive is telling the same thing as the original implication.

If  the origin is " p implies q", then the contrapositive is, by definition, "not q implies not p". If we transfer both to the form on con/disjunction, then the origin says the same thing as " not p or q" and the contrapositive says "q or not p", and that shows the reason for them to be equivalent.

 Fortunately, some properties and laws like De Morgan's Law and transitivity are pretty friendly. ( They didn't bother me at all!) We learned how to actually draw the truth by using venn diagram or tabulate the truth. Using these method all the properties we learned in the class can be proved and expressed in a clear way.

Some of the very last things we did before proving was the definition of limit. Limit is a very abstract concept and it is really hard to understand and even harder to write down. I've already learned something about limit in maths courses but to me it's nothing more than a vague concept. Ironically, it was in the computer science course that I completely understood the definition of the limit and how to actually prove limf(x)( x to a) = p.
The limit is just saying that if we make a number a extremely close to a value than we can make f(a) extremely close to another value. Like if we want to say lim n^2 goes to infinity, we define it as: for all c in real numbers, there exist a b in real numbers such that if n is larger than b n^2 is larger than c. This is, not exaggerating, an ingenious definition(at least by my point of view), because it let us pick any real number and not matter how large the real number we pick, we can always find n^2 larger than c, that ensures the function goes to infinity. However, if we switch the first two item: there exists a b, for all c, then the definition is not saying the same thing because now b can not rely on c anymore.