# [SOLVED] Is there a smallest real number that is greater than 0

• Feb 8th 2009, 01:46 PM
NeedHelp123
[SOLVED] Is there a smallest real number that is greater than 0
Not really a long question, but still kinda confusing. Thanks
• Feb 8th 2009, 01:48 PM
Jhevon
Quote:

Originally Posted by NeedHelp123
Not really a long question, but still kinda confusing. Thanks

no. to prove this, do a proof by contradiction. assume there is, show that you can find a smaller one

Quote:

Originally Posted by Moo
ahah ! 1-1

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• Feb 8th 2009, 01:50 PM
Moo
Quote:

Originally Posted by NeedHelp123
Not really a long question, but still kinda confusing. Thanks

No, there isn't.

Proof :
assume there exists such a number, m : $\forall x >0~,~0
Now consider $\frac m2$
This is obviously smaller than m. And still $>0$
So it's a contradiction.

ahah ! 1-1
• Feb 8th 2009, 01:53 PM
NeedHelp123
Hey guys thanks!