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SUMMARY

This discussion focuses on the effective use of quantifiers in mathematical statements, specifically addressing how to determine the truth value of statements involving integers. Participants emphasize the importance of translating statements accurately and understanding whether to provide a simple true/false answer or a counter-example for false statements. The example discussed involves the statement "for any integer n, there is some integer m such that n^2 < m," illustrating the need for critical thinking in evaluating such expressions.

PREREQUISITES
  • Understanding of mathematical quantifiers (universal and existential)
  • Basic knowledge of integer properties
  • Familiarity with logical reasoning and proof techniques
  • Ability to construct counter-examples in mathematical contexts
NEXT STEPS
  • Study the principles of mathematical logic and quantifiers in depth
  • Learn how to construct and evaluate mathematical proofs
  • Explore examples of true and false statements involving quantifiers
  • Practice creating counter-examples for various mathematical assertions
USEFUL FOR

Students of mathematics, educators teaching logic and proofs, and anyone looking to enhance their understanding of quantifiers and logical reasoning in mathematical contexts.

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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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