Originally Posted by **Rich B.**

Hi:

Now please don't get mad when I say this but, I agree with P.Hacker. Your arguments are well thought out, and you demonstrate a good working knowledge but, the argument seems to possess one flaw (and it is indeed possible that I am simply failing to comprehend something). Your opening statement is that which you are attempting to prove. That is, you have hypothesized the conclusion. Why go any further then? You were finished the moment you put the period at the end of the opening line.

Further, your closing statement for proof #1 is that 1>=cos(x). You seem to go to a lot of work in order to draw this conclusion, which you could have stated without argument, and no one would have batted an eye. Cos(x)<=1 is a simple extention of the definition of the cosine function. I.e., Cos(x) in [-1,1] for all real x implies Cos(x)<=1. Now, these things having been said, on what basis does cos(x)<=1 imply sin(x) + cos(x)>= 1? Please explain.

I close with this sincere and respectfully intended remark. P.Hacker sent his last post because he wanted to help you, not to elicit hostility and disrespect. Moreover, no, a proof is not complete until it works for the competent reader. We call it a proof because it establishes concurrence among the readership. ...for what it's worth.

Regards,

Rich B.