Question

( a - c, a ) U ( a, a + c ) can be written as

0 < | x - a | < c where c > 0

please explain how ?

Answer 1

inkyvoyd thanks that u r trying to give me solution :)

Answer 2

i have sent a file in here. open it u will find my problem

Answer 3

Ok, this set becomes (a-c,a,a+c)
|x-a|>0
x-a>0
or -x+a<0 ->x-a>0 (when you divide by a negative, switch the order of the "<"

|x-a|<c
x-a<c
or
a-x<c -> x-a<c

Answer 4

Thus, x-a>0, and x-a<c

Answer 5

meaning we can safely take away the absolute value symbol.

Answer 6

i have never seen 3 elements in open or closed interval

Answer 7

0<x-a<c
(x>a, x<a+c)
and set (a-c,a+c,0)

Answer 8

i am trying to understand all what so far u have sent me in written

Answer 9

Yes, It's been a while since I learned about set theory notation. Let me read that again >.<

Answer 10

( a - c, a ) U ( a, a + c )
in other words, the union of the interval (a-c,a) and (a,a+c)
so, we have the interval (a-c,a+c)

Answer 11

That is, if "(" is inclusive. It is, right?

Answer 12

no that is exclusive. [ ] it is inclusive

Answer 13

[bleep}

Answer 14

( a - c, a ) U ( a, a + c ) is not equal to (a-c,a+c)

Answer 15

|x-a|>0
x-a>0 or -x+a<0 ->x-a>0 (when you divide by a negative, switch the order of the "<"
both cases reduce to x-a>0
|x-a|<c
x-a<c or a-x<c -> x-a<c
both cases reduce to x-a<c

x-a>0
x-a<c
so, 0<x-a<c
or, a<x<c+a
Screw this, I give up. TIme to annoy others. @Callisto , @dpalnac ,

Answer 16

@dpalnac, inky wants ya
i admire the effort put in @inkyvoyd

Answer 17

inky ahahahahahah :D ... u didn't annoy me u helped me alot thanks a lot but still i'm trying to understand :) there is a problem
if | x - a | > 0 then -x + a > 0 this must be the case i think

Answer 18

I fail.

Answer 19

a<x<a+c
-a>x>-a-c

Answer 20

no u didn't fail it's ok. yah equlity changes when multiplying both side by neg

Answer 21

That's probably quite relevant, but I'm not sure where to go after that.

Answer 22

can u tell me in which mathematical course i can learn full about inequality ?

Answer 23

plz read this : can u tell me in which mathematical course i can learn full about inequality with absolute operation ?

Answer 24

Oh, look at these links (lemme find them)

Answer 25

such things creat big problem for me

Answer 26

sure i wait :)

Answer 27

I like purple math, so I think this should work
http://www.purplemath.com/modules/absineq.htm

Answer 28

SOS math is pretty good too
http://www.sosmath.com/algebra/inequalities/ineq03/ineq03.html

Answer 29

yah... that is great site.. u r right.. thanks a lot i try now to learn something from there :)

Answer 30

once again thanks .. now i go to that site ... see u frnd :)

Answer 31

You too :)

Answer 32

:) :)