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Mathematics
Set Theory, Logic, Probability, Statistics
Upper Bound of Sets and Sequences: Analyzing Logic
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[QUOTE="solakis1, post: 6784447, member: 703897"] The complete and correct [B]formalization [/B]of the above statatments are the following : 1)$M\in R$ is an upper bound of $A\subseteq R$ iff (and not if) $\forall a(a\in A\Rightarrow a\leq M)$ 2)$M\in R$ is an upper bound of the sequence $(a_n)$ iff $\forall n ( a_n\leq M)$ OR 1)A, $A\subseteq R$ is bounded from above iff ) $\forall a((a\in A\Rightarrow\exists M(M\in R\wedge( a\leq M))$ 2) $(a_n)\subseteq R$ is bounded from above iff $\forall n\exists M (M\in R\wedge (a_n\leq M)$ So depending on the words of the definition there different ways to formalise the definition Also you [B]do not use logic[/B] for formalizing a mathematical statement To prove that two statement are [B]equivalent you have to use logic[/B] Now according to the words expressing that A has an upper bound M you can use the appropriate formalization [/QUOTE]
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Mathematics
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Upper Bound of Sets and Sequences: Analyzing Logic
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