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   When is a set bounded from above?

   • A set S of real numbers is called bounded from above if there exists some real number k (not necessarily in S) such that k ≥ s for all s in S. The number k is called an upper bound of S. The terms bounded from below and lower bound are similarly defined. A set S is bounded if it has both upper and lower bounds.

   Bounded set - Wikipedia

   en.wikipedia.org/wiki/Bounded_set

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   What does it mean when a function is bounded above?

   • A function is bounded from above if there exists a real number, k, such that for all x, . The number k is called the upper bound. For example, the peak point is the upper bound in the above example.

   Bounded Functions | Superprof

   www.superprof.co.uk/resources/academic/maths/calculus/functions/bounded-functions.html

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   What if a is bounded above or below?

   • Case 2. If A = B A = B than every element in A A is in B B. This implies that if A A is bounded above or below so is B B and vice versa. If the sup B B is defined to be the least upper bound and the inf B B is defined to be the greatest lowest bound. Than sup B B = sup A A and inf B B = inf A A.

   Show that if $A\\subseteq B$, then inf $B\\leq$ inf $A\\leq$ sup $A

   math.stackexchange.com/questions/528089/show-that-if-a-subseteq-b-then-inf-b-leq-inf-a-leq-sup-a-leq-sup-b

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   What is boundedness in math?

   • What is boundedness? Boundedness is about having finite limits. In the context of values of functions, we say that a function has an upper bound if the value does not exceed a certain upper limit. More... Other terms used are "bounded above" or "bounded below".

   Boundedness - Precalculus - Socratic

   socratic.org/precalculus/functions-defined-and-notation/boundedness

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   What if p x a is bounded above?

   • (∀x ∈ A) p ≤ x A is bounded above (or right bounded) iff there is q ∈ F such that (∀x ∈ A) x ≤ q In this case, p and q are called, respectively, a lower (or left) bound and an upper (or right) bound, of A. If both exist, we simply say that A is bounded (by p and q).

   2.4: Upper and Lower Bounds. Completeness - Mathematics LibreTexts

   math.libretexts.org/Bookshelves/Analysis/Mathematical_Analysis_(Zakon)/02:_Real_Numbers_and_Fields/2.04:_Upper_and_Lower_Bounds._Completeness

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   What does 'bounded' mean in this context?

   • The term 'bounded' does not apply to the context provided. In this passage, Wordsworth is discussing the topic of law becoming vital and engaging during the French Revolution. The passage does not contain the definition or usage of the word 'bounded' as given in the question.

   Tintern Abbey and The Prelude Test Study Guide Flashcards

   quizlet.com/316736636/tintern-abbey-and-the-prelude-test-study-guide-flash-cards/

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2. socratic.org › questions › what-does-bounded-aboveWhat does bounded above or below mean in precaculus?

   socratic.org › questions › what-does-bounded-above

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   Apr 25, 2017 · Definitions: A set is bounded above by the number A if the number A is higher than or equal to all elements of the set. A set is bounded below by the number B if the number B is lower than or equal to all elements of the set.

3. socratic.org › boundednessBoundedness - Precalculus - Socratic

   socratic.org › boundedness

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   Key Questions. What is boundedness? Answer: Boundedness is about having finite limits. In the context of values of functions, we say that a function has an upper bound if the value does not exceed a certain upper limit. More... Explanation: Other terms used are "bounded above" or "bounded below".

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5. math.stackexchange.com › questions › 299229What does it mean when you say that the function is bounded?

   math.stackexchange.com › questions › 299229

   Feb 10, 2013 · Bounded means bounded above and below. The function −x2 − x 2 is not bounded. In most applications to algorithms, it doesn't matter, since the functions are naturally non-negative, so are bounded below by 0 0. But in principle one should be careful.

6. math.libretexts.org › Bookshelves › Analysis2.4: Upper and Lower Bounds. Completeness - Mathematics ...

   math.libretexts.org › Bookshelves › Analysis

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   A is bounded above (or right bounded) iff there is q ∈ F such that. (∀x ∈ A) x ≤ q. In this case, p and q are called, respectively, a lower (or left) bound and an upper (or right) bound, of A. If both exist, we simply say that A is bounded (by p and q).

7. library.fiveable.me › key-terms › calc-iiBounded above - (Calculus II) - Vocab, Definition ... - Fiveable

   library.fiveable.me › key-terms › calc-ii

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   Definition. A sequence is said to be bounded above if there exists a real number M such that every term in the sequence is less than or equal to M. The smallest such M is called the least upper bound or supremum.

8. mathworld.wolfram.com › BoundedfromAboveBounded from Above - Wolfram MathWorld

   mathworld.wolfram.com › BoundedfromAbove

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   5 days ago · Bounded from Above. A set is said to be bounded from above if it has an upper bound. Consider the real numbers with their usual order. Then for any set , the supremum exists (in ) if and only if is bounded from above and nonempty.

9. math.stackexchange.com › questions › 2015627terminology - "bounded from above" vs. "bounded above ...

   math.stackexchange.com › questions › 2015627

   1. For unary functions f, g: X → Y f, g: X → Y, where X X is any set and (Y, ≤) (Y, ≤) is a poset, when you rephrase ∀x∈X: f(x) ≤ g(x) ∀ x ∈ X: f (x) ≤ g (x) in prose, do you write. " f f is bounded above by g g " or. " f f is bounded from above by g g " or. " f f is majorized by g g "? Why?