What is the difference between $f(x_1) \geq f(x_2)$ and $(f(x_1) > f(x_2))$?

Question

I am studying for my math course and I come across this definition.

I am really struggling to understand the difference the parentheses make in the inequality. Can somebody please explain and why?

Thank you.

Sorry what I meant is what is the difference between f(x1) > f(x2) and (f(x1) > f(x2)). Like what difference does the fact that the f(x1) > f(x2) are closed in the parentheses make? (the right part of the inequality) — , Nov 07 '17 at 10:26

score 6 · Accepted Answer · 2017-11-07T10:26:38.193

6

You're misreading. This whole paragraph follows the general pattern for saying two similar things at the same time.

____ X (or Y) ____ P (or Q) ____

which means both

____ X ____ P ____

and

____ Y ____ Q ____

The first inequality is only meant to appear in the first meaning, and the second (parenthesized) inequality is only meant to appear in the second meaning.

edited Nov 07 '17 at 10:26

answered Nov 07 '17 at 10:25

2

the number of blah's make this oddly difficult to read – user363464 Nov 07 '17 at 10:26
@user363464: I agree and appreciate the second opinion! – Nov 07 '17 at 10:27
This makes perfect sense, thank you very much :) – Nov 07 '17 at 10:28
Use If and then instead of ____? – Did Nov 07 '17 at 10:29
This is probably a matter of personal taste but I tend to prefer the use of respectively Y rather than or Y. I think that the latter can be a bit misleading in some cases. – M. P. Nov 07 '17 at 10:40

score 4 · Answer 2 · answered Nov 07 '17 at 10:25

4

This is a shortcut used by many textbooks. We define both decreasing and strictly decreasing at the same time. Because their definitions are the same, except for the $\geq$ and $>$, the author used parentheses to differentiate between the two cases.

answered Nov 07 '17 at 10:25

Stefan

3,451

omg thank you very much, I always tend to mess up like this :) – Nov 07 '17 at 10:27

What is the difference between $f(x_1) \geq f(x_2)$ and $(f(x_1) > f(x_2))$?

2 Answers2