Week 5 and 6

In the fifth and sixth week, my professor covered how to write proofs for various mathematical statements. This includes formatting them by logically indenting them, commenting them and concluding them with the original statement. Proofs take a lot of time to structure and write because you must consider all possible situations for where the mathematical equation is true or false. Some proofs though, are quick to prove. For example:        $xeR, x ** 3 + 3x ** 2 - 4x = 12
This is an existential, so it is not hard to prove. But you must find the right term to prove it true. This is where it sometimes gets tricky, as you may have to conduct a trial and error method before finding the right term.
So, in this, when x = 2, the existential proves to be true. This is written as:
                                    Pick x = 2. Then xeR    # well known
                                    Then x ** 3 + 3x ** 2 - 4x = 8 + 12 - 8
                                                                                = 12              # sub 2 for x
                                    Then $xeR, x ** 3 + 3x 
This is an example of how a proof is written.

My professor continued teaching us how to write more proofs after this, especially those with floor division of x (ëxû). But, he also reemphasized a limit and its graph and taught us how to write a proof based on limits.
At first, I had difficulty understanding how to write proofs, what conditions to include and how to indent them, but now I have started to understand it. Writing proofs seems simpler for me than it used to because I have learnt that you just have to follow a certain logical order by looking at the mathematical expression.