## anonymous 4 years ago I have a question about notation. Just let me write it out.

1. anonymous

$3x^2 >= 0$ $\forall x$ (three dots like a triangle upside down) x^2 is always positive. Sorry for the line spacing, it should all be on one line. Would this read: "3x^2 is more than or equal to 0 for all x because x^2 is more than or equal to zero" ?

2. precal

|dw:1328399150129:dw|

3. anonymous

Thank you, but it was the latter part I wasn't sure about. For all x And the triangle ( http://en.wikipedia.org/wiki/Because_sign )

4. Zarkon

$3x^2\ge0 \hspace{.5cm}\forall x,\hspace{.2cm}\because x^2\ge 0$

5. anonymous

Thank you! Is that correct notation? I mean would it "grammaticly" correct?

6. precal

are you trying to do set builder notation?

7. Zarkon

yes

8. precal

Are you trying to determine the solution of that inequality?

9. anonymous

The original problem was. Prove that x^3 - ax is increasing for all x if a < 0 But I wanted to use proper notation.

10. precal

|dw:1328399454066:dw|

11. precal

|dw:1328399493672:dw|

12. precal

Is this calculus, where you are proving intervals that are increasing and decreasing?

13. anonymous

Yes this calculus, but the calculus wasn't the problem, it was just the notation

14. precal

Usually when you are asked to prove an increasing or decreasing interval. Step 1: You take the derivative of the given function Step 2: You take that equation and set it equal to zero and solve the solutions that are positive represent increasing the solutions that are negative represent decreasing I am not sure you were on the correct track Nevermind what you solution is, the professor would have realized that you were not doing the problem correctly. Stating the wrong solution correctly does not make the solution correct. In mathematics we look for the correct process, correct solutions and correct mathematical notation ie set builder notation