Post Four

Term Test Two

    I thought this test was well written and even easier than the first. That being said I still managed to get, what I consider the easiest of the three questions given, wrong. My main mistake was fairly simple, I completely disregarded the negation of the statement mid proof and made an assumption for q rather than very simply showing its existence, q being the first q in the statement. My reasoning behind it at the time was that the value of this q in and of itself was irrelevant in the overall proof. That is, I did not need to directly use it when showing there are no q2, q2 being the other q in the statement, such that m= … But, as should be obvious to most readers, my opinion of the values relevancy is in itself irrelevant. Because I was, in the negation of the original statement, claiming that there existed a q I was thereby obligated to clearly show its existence regardless of its usefulness or obviousness. On the bright side though, I can certainly say that I'll never make the same mistake again.

    Another interesting thing about my test is the answer I gave for the third question. Mine was different than sample solution provided. That is because I decided to, out of comfort with the method itself, prove the statement by contradiction rather than directly. Looking back, the direct proof is only, at least in my case, marginally easier. To prove the given statement by contradiction I simply showed that if floor(x) + 7 <= x + 6 then there exists a z, in this case floor(x) + 1, that proves the negation of the definition of floor which is a contradiction. The reason I say that the solution provided gives only a marginally easier proof is because I encountered a statement similar to this one where contradiction was used in the proof prior to the test so I already knew exactly what to do to prove it by using contradiction.