The Student Room Group
Uni students - Complete our survey >>
Uni students - Complete our survey >>
Uni students - Complete our survey >>

This discussion is now closed.

Check out other Related discussions

wahey...proof by contradiction!

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?
Reply 1
Avatar for Leekey
Leekey
9
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?!? :confused:
Reply 2
Avatar for john !!
john !!
14
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.
Reply 3
Avatar for lgs98jonee
lgs98jonee
2
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
and wot about (a1+x)/2=


so we have a contradiction
Reply 4
Avatar for Jonny W
Jonny W
8
Let x be the smallest nonzero rational between 0 and 1. Then x/2 is a smaller nonzero rational between 0 and 1. Contradiction.
Reply 5
Avatar for rae
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

????????
Reply 6
Avatar for hohum
hohum
OP
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!
Reply 7
Avatar for S@sha
S@sha
7
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.
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! :smile: I know the proble has beeen solved but I thought i'd put in my two pence

MB
Reply 9
Avatar for Jonny W
Jonny W
8
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! :smile: 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.
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
Reply 11
Avatar for S1M
S1M
Jonny W
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! :smile: 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...

Related discussions

Latest

Trending

Trending

Articles for you