Logical expression using quantifiers

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Homework Help Overview

The discussion revolves around expressing a statement about the existence of a smallest positive real number using logical expressions and quantifiers. The original poster attempts to formulate this expression and clarify the universe of discourse as positive real numbers.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore different formulations of the logical expression, with some suggesting alternative representations. There is a focus on the negation of the existence of a smallest positive number and the implications of the original statement.

Discussion Status

Participants are actively engaging with the original poster's attempt, offering alternative expressions and questioning the clarity of the statements made. There is an ongoing examination of the logical structure and assumptions involved in the problem.

Contextual Notes

There is a noted confusion regarding the interpretation of the original statement and its negation, as well as the order of posts affecting the clarity of responses.

mutzy188
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Homework Statement



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

There is no smallest positive real number

The Attempt at a Solution



(∃y)((∀x)(y<x) )x

universe of discourse: poaitive real numbers

Is this correct?

Thanks
 
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Why not just write: \forall x &gt; 0,\;\exists y &gt; 0:y &lt; x
 
Last edited:
Your statement says that there is a smallest positive number. You want to take the negation of that.
 
ZioX said:
Your statement says that there is a smallest positive number
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:
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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