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4. Translate the following definition in symbols. "The limit of the function f(r) as r approaches infinity is L if and only if for all positive number e, there exists a natural number n such that the distance between f(x) and L is less than e whenever r is greater than n."

4. Translate the following definition in symbols. "The limit of the function f(r) as r approaches infinity is L if and only if for all positive number e, there exists a natural number n such that the distance between f(x) and L is less than e whenever r is greater than n."

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Use a two-column proof to prove the equivalence below -(PV-Q) v (-P-Q) = ¬P 2. Provide a negation for each statement. The negations should be in simplest form, i.e., there are no negations before a quantifier nor prior to a compound statement. (a) Some integers are either prime or composite. (b) Any non-negative number that is smaller than any positive number is zero. 3. Let S be the set of BS Math students, M be the set of math courses/subjects, and p(s, m) be the predicate on Sx M which states that "s likes m". Express the following in symbols. (a) Someone does not like any kind of math course. (b) Nobody likes all kinds of math courses. (c) Some math course is liked by everyone. (d) There is a math course that nobody likes. 4. Translate the following definition in symbols. "The limit of the function f(r) as r approaches infinity is L if and only if for all positive number e, there exists a natural number n such that the distance between f(x) and L is less than e whenever r is greater than n."
Transcribed Image Text:1. Use a two-column proof to prove the equivalence below -(PV-Q) v (-P-Q) = ¬P 2. Provide a negation for each statement. The negations should be in simplest form, i.e., there are no negations before a quantifier nor prior to a compound statement. (a) Some integers are either prime or composite. (b) Any non-negative number that is smaller than any positive number is zero. 3. Let S be the set of BS Math students, M be the set of math courses/subjects, and p(s, m) be the predicate on Sx M which states that "s likes m". Express the following in symbols. (a) Someone does not like any kind of math course. (b) Nobody likes all kinds of math courses. (c) Some math course is liked by everyone. (d) There is a math course that nobody likes. 4. Translate the following definition in symbols. "The limit of the function f(r) as r approaches infinity is L if and only if for all positive number e, there exists a natural number n such that the distance between f(x) and L is less than e whenever r is greater than n."
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