# Logical expression using quantifiers

1. Sep 8, 2007

### mutzy188

1. The problem statement, all variables and given/known data

Express each statement as a logical expression using quantifiers. State the universe of discourse.:

There is no smallest positive real number

3. The attempt at a solution

(∃y)((∀x)(y<x) )x

universe of discourse: poaitive real numbers

Is this correct?

Thanks

2. Sep 9, 2007

### bomba923

Why not just write: $$\forall x > 0,\;\exists y > 0:y < x$$

Last edited: Sep 9, 2007
3. Sep 9, 2007

### ZioX

Your statement says that there is a smallest positive number. You want to take the negation of that.

4. Sep 9, 2007

### bomba923

No, my statement does not say that at all.

*Edit: If your post was directed at the OP, please state so in your post; else, your assertion is clearly false (your post comes directly after mine, so I assume you are referring to my post)

Last edited: Sep 9, 2007
5. Sep 9, 2007

### HallsofIvy

Staff Emeritus
It is quite possible that ZioX wrote his reply before yours was posted- he thought his would appear immediately after mutzy188's post. Of course, you are right. It would have been clearer if he (and you- your reply might well have wound up after his) had copied the original post into the response.

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