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#1 2005-12-31 23:15:39

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Function that dicsern the numbers?

I need a function dic(x) that gives 1 when x is rational and 0 when it's irrational.
Please give me some advice.
I think there will exist such.


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#2 2006-01-01 00:09:38

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,551

Re: Function that dicsern the numbers?

You could prove a number is rational by discovering the ratio (example: 1.5 is 3/2, hence rational)

And there are various proofs for irrational numbers.

But there are also "Open Questions", see Wikipedia Article (near end), so the best you could do (using current knowledge!) would be:

disc(x) = 1 when rational
disc(x) = -1 when irrational
disc(x) = 0 when unknown

Now, a computer program could run through thousands of decimal places looking for a repeating pattern and never discover it, but that would not prove anything - it could still be the ratio of two very large numbers!


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#3 2006-01-01 05:21:49

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: Function that dicsern the numbers?

I found something:
Number r is:
1.Rational, if the function

is periodic
2.Irrational, when HS_r[x] is not a periodic function.

Last edited by krassi_holmz (2006-01-01 05:23:42)


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#4 2006-01-01 05:28:04

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: Function that dicsern the numbers?

But it's useless, because I don't know non-trivial terms for a function to be periodic.


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