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Discussion Overview

The discussion revolves around understanding quantifiers in mathematical statements, specifically how to express truth values and the necessity of providing counterexamples. Participants explore the implications of statements involving integers and the conditions under which they can be deemed true or false.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • Some participants inquire about the nature of answers regarding quantifiers, questioning whether they should provide all truth values or a single value.
  • Others emphasize the importance of translating statements accurately as a foundational step in understanding their truth values.
  • One participant suggests that if a statement is true, it should simply be stated as such, while if false, a counter-example should be provided.
  • Another participant illustrates the process by discussing a specific statement involving integers and encourages others to consider various integer values to assess the truth of the statement.

Areas of Agreement / Disagreement

Participants express differing views on whether a complete answer requires only a true or false designation or if counterexamples are necessary. The discussion remains unresolved regarding the best approach to expressing answers related to quantifiers.

Contextual Notes

Participants demonstrate varying levels of understanding regarding the translation of statements and the requirements for expressing truth values, indicating potential gaps in foundational knowledge.

annie1
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Re: quantifiers

What progress have you made on any of these?
Can you tell us what sort of help you need?
 
Re: quantifiers

in these i don't understand how to express the answer of any of the following ,can i tell all the truth values or some single,if so then how
 
Re: quantifiers

annie said:
in these i don't understand how to express the answer of any of the following ,can i tell all the truth values or some single,if so then how

Well then, you must spend some time learning to translate each statement. That is the first step.

For example: the statement in a) says "for any integer $$n$$, there is some integer $$m$$ such that $$n^2<m$$.
Is that true or false?
 
Re: quantifiers

i understand the symbols and the meaning of the statements but i want to know the answer is only true or false or i have to give counter example to express it completely
 
Re: quantifiers

annie said:
i want to know the answer is only true or false or i have to give counter example to express it completely

If the statement is true then say so.
If it is false then give a counter-example.
 
Re: quantifiers

Plato said:
For example: the statement in a) says "for any integer $$n$$, there is some integer $$m$$ such that $$n^2<m$$.
You'll have to think about the meaning of these statements; there is no way around it. For example, for $n=5$, can you find an integer $m$ such that $n^2=25<m$? What about for $n=0$, $n=-5$ and every other integer $n$?
 

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