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Q: Monotone convergence theorem is true for decreasing sequence?
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Define a monotone sequence of real numbers?

A monotone increasing sequence {r_n | n>0} is a sequence with: n>m implies r_n >= r_m A monotone decreasing sequence {r_n | n>0} is a sequence with: n>m implies r_n <= r_m A strictly monotone increasing sequence {r_n | n>0} is a sequence with: n>m implies r_n > r_m A strictly monotone decreasing sequence {r_n | n>0} is a sequence with: n>m implies r_n < r_m Theorem. All bounded monotone sequences of real numbers have a unique limit.


Is Bolzano-Weierstrass theorem for sets equivalent to the completeness theorem?

Yes, it is, as are all the following: Completeness Axiom Heine-Borel Nested Set Bolzano-Weierstrass Monotone Convergence


Sequence of steps that leads to a valid conclusion as for the theorem?

proof


What is a theorem?

A theorem is a math term used to describe an idea that can be proved.A mathematical statement which has been proved trueIt is a statement or proposition which can be derived from a set of axioms and following a sequence of logical reasoning.


Geometrical meaning of derivation?

the process of deducing a new formula, theorem, etc., from previously accepted statements. • a sequence of statements showing that a formula, theorem, etc., is a consequence of previously accepted statements.


What did Mary Lucy Cartwright discover?

Mary Lucy Cartwright was a British mathematician who made significant contributions to the field of chaos theory and differential equations. She is well-known for her work on the Cartwright-Littlewood theorem, which provides a criterion for the convergence of Fourier series.


What is norton's theorem?

Norton's theorem is the current equivalent of Thevenin's theorem.


How do you solve a remainder theorem?

You cannot solve a theorem: you can prove the theorem or you can solve a question based on the remainder theorem.


What are the aspects of Pythagoras theorem?

There are 19 various aspects of Pythagoras theorem. Pythagorean Theorem (1) Pythagoras Theorem(2) Pythagorean Theorem (3) Pythagorean Theorem (4) Pythagoras Theorem(5) Pythagorean Theorem(6) Pythagrean Theorem(7) Pythagoras Theorem(8) Pythagorean Theorem (9) Hyppocrates' lunar Minimum Distance Shortest Distance Quadrangular Pyramid (1) Quadrangular Pyramid (2) Origami Two Poles Pythagoras Tree(1) Pythagoras Tree(2) Theorem by Pappus


What type of statement must be PROVEN in geometry?

That is a theorem.A theorem.


What is the definition of theorem in geometry?

theorem


Can a theorem be proven using a corollary?

No, a corollary follows from a theorem that has been proven. Of course, a theorem can be proven using a corollary to a previous theorem.