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1. using proof by contradiction, show that there are an infinte number of rational numbers between 0 and 1.

I can never do these...is there a standard method to follow?
2. (Original post by hohum)
using proof by contradiction, show that there are an infinte number of rational numbers between 0 and 1.

I can never do these...is there a standard method to follow?
This is one of those a/b things int it?!?
3. (Original post by hohum)
using proof by contradiction, show that there are an infinte number of rational numbers between 0 and 1.

I can never do these...is there a standard method to follow?
If there isn't an infinite amount, say there are n rational numbers, with m/n the highest, where 0<n and 0<m, and n>m. But consider (m+1)/(n+1), this is another larger rational number between 0 and 1, so contradiction.
4. (Original post by mik1a)
If there isn't an infinite amount, say there are n rational numbers, with m/n the highest, where 0<n and 0<m, and n>m. But consider (m+1)/(n+1), this is another larger rational number between 0 and 1, so contradiction.
surely assume there are a finite number between 0 and 1 namely
a1, a2, a3......1

ok but wot does (a1+a2)/2=???x??
we have new one

5. Let x be the smallest nonzero rational between 0 and 1. Then x/2 is a smaller nonzero rational between 0 and 1. Contradiction.
6. can you say:

assume there is a finite number blah...

n / n+1 where n can take any +ve integer

therefore there is a finite number of rational numbers as n is infinite itself

????????
7. (Original post by rae)
can you say:

assume there is a finite number blah...

n / n+1 where n can take any +ve integer

therefore there is a finite number of rational numbers as n is infinite itself

????????
Oh great you're all stupidly clever compared to me! Thanks though, I see your thinking even if I can't think it myself!
8. (Original post by Jonny W)
Let x be the smallest nonzero rational between 0 and 1. Then x/2 is a smaller nonzero rational between 0 and 1. Contradiction.
that's a nice one. I like that one.
9. (Original post by Jonny W)
Let x be the smallest nonzero rational between 0 and 1. Then x/2 is a smaller nonzero rational between 0 and 1. Contradiction.
Or of course the opposite. let x be the greatest rational number between 0 and 1 (non inclusive) x^2 is a bigger rational number! I know the proble has beeen solved but I thought i'd put in my two pence

MB
10. (Original post by musicboy)
Or of course the opposite. let x be the greatest rational number between 0 and 1 (non inclusive) x^2 is a bigger rational number! I know the proble has beeen solved but I thought i'd put in my two pence
x^2 < x, so your proof isn't the opposite.
11. (Original post by Jonny W)
x^2 < x, so your proof isn't the opposite.
In fact its not even a proof. Surely it should be if x is the greatest rational number with 0<x<1, then what is (x+1)/2 ? Well its greater then x , contradiction
12. (Original post by Jonny W)
(Original post by musicboy)
Or of course the opposite. let x be the greatest rational number between 0 and 1 (non inclusive) x^2 is a bigger rational number! I know the proble has beeen solved but I thought i'd put in my two pence

MB
x^2 < x, so your proof isn't the opposite.
can't you call x the lowest rational number instead? then x^2 is lower...

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