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Prove that if a real sequence is bounded and monotone it converges?
A bounded and monotone sequence must converge due to the Monotone Convergence Theorem. If the sequence is monotonically increasing and bounded above, it approaches a least upper bound (supremum), while if it is monotonically decreasing and bounded below, it approaches a greatest lower bound (infimum). In either case, the sequence will converge to its supremum or infimum, respectively, demonstrating that any bounded monotone sequence converges.
What is an example of a function that is of bounded variation but not Lipschitz continuous?
How about f(x) = floor(x)? (On, say, [0,1].) It's monotone and therefore of bounded variation, but is not Lipschitz continuous (or even continuous).
Does a parallelogram have 2 sets of parallel sides?
Yes, that can be considered the definition of a parallelogram.Yes, that can be considered the definition of a parallelogram.Yes, that can be considered the definition of a parallelogram.Yes, that can be considered the definition of a parallelogram.
term?
what does DNA stand fordeoxyribonucleic acidwhere in the cell are chromosomes locatedin the nucleus
What is the definition of measure of an angle?
give the definition of an andle
What does monotone?
It means to have only one tone.See the related link listed below for the definition:
What sentence can be use with the word monotone?
She had a monotone voice.
How can the word monotone be used in a sentence?
the word monotone can be used in a sentece like this: "i dont know what monotone means"
What is a sentence with monotone in it?
I wouldn't have fallen asleep if the speaker had used something more than a monotone. The monotone humming of the engine soon lulled me to sleep.
What is the part of speech of monotone?
"Monotone" is fundamentally a noun, but in mathematics it is sometimes used as an adverb, as in the sentence, "This function is monotone increasing."
Can you write a sentence with the word monotone?
The Headmaster addressed the assembly in a monotone voice
When was Monotone - software - created?
Monotone - software - was created on 2003-04-06.
When was Monotone - Record Label - created?
Monotone - Record Label - was created in 2001.
Use monotone in a sentence?
The long musical phrase was just a monotone, playing at the same pitch for some time The monotone was scary.
How would you use monotone in sentence?
You could use the word monotone in a sentence like this: When the man spoke he was very monotone. monotone means a single tone without harmony or variation so basically it means boring.
Use a sentence with the word monotone?
My professor always has a monotone voice every morning.Since my grandfather is so old,he always speaks in a very monotone voice.
How do you get monotone chao on sonic DX?
monotone chaos are the chao that you buy from the black market
