5.4-5.5, due on February 6

I had difficulty understanding the existence proof regarding irrational numbers and the one involving the square root of 2 to the power of square root of two.  I agreed that the proof seemed unsatisfactory since two specific irrational numbers a and b were not identified to confirm a^b was rational.  It would have been far easier to understand if specific numbers were given to produce the desired result.  To prove it in theory was hard to comprehend, but a crafty way, I suppose, in proving the result without giving two actual numbers.

I noticed that I had recently studied about the Intermediate Value Theorem of Calculus in Math 112.  That tied in nicely to something I just studied.  It made sense and in the Calculus homework we had to prove that an equation set to equal zero had a solution within a certain interval.  I remember that I threw together some sort of rough proof and called it good, but now I believe I have the capacity to produce a more sophisticated and thorough proof.  It would have been nice for that assignment.  I think it was fine, though, because, from what I could tell, not many of the Math 112 students in my class had skill mastery in proofs.  This Math 290 class is beneficial.