annie1
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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.
PREREQUISITESStudents of mathematics, educators teaching logic and proofs, and anyone looking to enhance their understanding of quantifiers and logical reasoning in mathematical contexts.
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
annie said:i want to know the answer is only true or false or i have to give counter example to express it completely
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 $n$?Plato said:For example: the statement in a) says "for any integer $$n$$, there is some integer $$m$$ such that $$n^2<m$$.