Question

I need help with a proof. I believe I ave it mostly correct but I did something illegal in it.

Answer 1

ha!! you have a very nice hand writing

Answer 2

lol my girlfriend and I are in the same class, took a picture of hers because my writing is horrid

Answer 3

I can't help sorry but that's funny :) at least your honest :D

Answer 4

I'm a little troubled by the removal of \(\sqrt{x}\). If \(\sqrt{x} = 0\), the appearance of the strict inequality is not appropriate. You have two ways to solve this. I'm not telling. (Well, at least right away.)

Answer 5

I do not like your closing statement. If you are going to accept it "by definition", why did you go to all the trouble to prove it. The words "by definition" do not belong in this context.

Answer 6

You're saying your name is not "Sarah", Derek?

Answer 7

there is another picture with mine, my writing is horrible which is why the other picture.

Answer 8

Okay, let's see if you can address the first concern. Is Sarah there to discuss it with you?

Answer 9

no

Answer 10

she's at her place

Answer 11

Two opinions would be better. In any case, we have two things that can be done.

1) Assume that as x approaches c, x is eventually nowhere near zero. This is often written \(x \gg 0\). All we really need is \(x > 0\), but the other one is a little more clear. If we establish this, by simply stating it, then the statement \(|\sqrt{c}| < |\sqrt{x} + \sqrt{c}|\) is exactly correct.

2) Alternatively, and this might seem a WHOLE LOT simpler, one can merely state \(|\sqrt{c}| \le |\sqrt{x} + \sqrt{c}|\), since it might be the case in the travels of our wandering x, that \(x = 0\). However, without the strict inequality, will the proof seem less satisfactory?

Points to ponder!

Answer 12

knew we did something wrong. but it's late here, gonna have to revisit the problem tomorrow

Answer 13

Good work. Don't forget my second concern.