Cool, though it seems like doing the three cases is unnecessary. I am not sure how your case 1 is using that 0 < a (the statement already gives you a 0)
I believe you are right! I just wanted to make sure that it was clear why this theorem works, regardless of where a and b are placed on the real line. Of course, with the stipulation that a
I believe it is important to show why something is true, even if it is obvious. It also develops the subject from its axiomatic foundations. From the Axiom of Completeness, we proved the Archimedean Principle, and from that we proved this.
nice
For the inequality na
Suppose na=.5 (1+na=1.5), then .5
Oh yeah. It’s all coming together
Cool, though it seems like doing the three cases is unnecessary. I am not sure how your case 1 is using that 0 < a (the statement already gives you a 0)
I believe you are right! I just wanted to make sure that it was clear why this theorem works, regardless of where a and b are placed on the real line. Of course, with the stipulation that a
Is there a point to proving these obvious results other than practicing notation?
I believe it is important to show why something is true, even if it is obvious. It also develops the subject from its axiomatic foundations. From the Axiom of Completeness, we proved the Archimedean Principle, and from that we proved this.
he's working through the formalism of real analysis...I love it