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General Forum: Education | | ******MATHEMATICS****** | |
| Reposting the question :
Divide the set of positive real numbers into three subsets, such that the equation
"a + b = 5c"
is not solvable in any of the subsets, i.e. the equation does ot hold, for any three numbers a, b, c, that come from the same subset.
Posted by: Raj Sekhar At: 13, Nov 2003 3:16:47 PM IST
hello sreeram garu.....the problem is to divide the entire positive real numbers not just only "natural numbers"
ayinaa....mee answers three subsets gaa wraayandi,so that it will be clear....
Posted by: Raj Sekhar At: 13, Nov 2003 3:15:02 PM IST
well....divide the whole continnum into
x where x/5=0
(x-1) (x-2) (x-3) (x-4)
add up (x-1) and (x-3) into one group
(x-2) and (x-4) into one group
pick up all numbers from x corresponding to the forula 5a and dump in the other groups
ex......in natural numbers u get 5 10 15 20 25 etc pick up 5*5, 5*10, 5*15 so on and dump in any other subset you want
does it work???
Posted by: Mr. sreeram katakam At: 13, Nov 2003 3:10:02 PM IST
asalu first of all....cheyyamannadi +ve real numbers ki...natural numbers ki kaadu.....
next thing....poni,if u have done it for natural numbers......even then also....some probs...
1st set :
1 + 19 = 4*5....
1,19 and 5 are from this subset only
2nd set :
2 + 23 = 5*5
2,23 and 5 r from this ame subset
3rd set :
3 + 27 = 5*6
3,27 and 6 are from this same subset
.....(like that,we can find infinite contradictory cases....)
Posted by: Raj Sekhar At: 13, Nov 2003 1:58:17 PM IST
hmmm....its not unique way........naaku thelisina procedure prakaaram,infinite solutions cheppocchu....
Posted by: Raj Sekhar At: 13, Nov 2003 1:04:26 PM IST
Raj, am curious is there a unique way of such distribution into subsets ?
Posted by: Mr. Frank Abagnale Jr. At: 13, Nov 2003 11:38:26 AM IST
actually.....i feel this is really a tough question for me atleast......somebody asked me......i found it interesting,and posted here...
hint :
hmmm....elaa ivvaalo theliyadu...
divide into many small subsets with min and max value of subsets choosing such that the equation is unsolvable....and then distribute those subsets into three groups....
Posted by: Raj Sekhar At: 10, Nov 2003 11:07:04 PM IST
interesting qsn indeed. Can u gimme a hint . I remember doing some sort of continuity on the real line in the analysis course. I am sure this has to do with something of that sort.
Thanks
Posted by: Mr. Frank Abagnale Jr. At: 10, Nov 2003 10:58:33 PM IST
Chaalaa break tharuvaatha oka manchi question :
Divide the set of positive real numbers into three subsets, such that the equation
"a + b = 5c"
is not solvable in any of the subsets, i.e. the equation does ot hold, for any three numbers a, b, c, that come from the same subset.
Posted by: Raj Sekhar At: 10, Nov 2003 7:51:50 PM IST
oohh....good right.......
Posted by: Raj Sekhar At: 30, Oct 2003 10:04:18 PM IST
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