In each part of this question, you are asked to give an example of something, and explain why it is an example. You may use all definitions, lemmas, theorems etc. from the lecture notes. (a) A sequence (an) such that, for every natural number , there exists a subsequence (an) of (an) converging to l. (You may use without proof that there exists a bijective function f: N→ NX N.)

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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In each part of this question, you are asked to give an example of something, and explain why
it is an example. You may use all definitions, lemmas, theorems etc. from the lecture notes.
(a) A sequence (an) such that, for every natural number , there exists a subsequence (an)
of (an) converging to l. (You may use without proof that there exists a bijective function
f: N→ NX N.)
Transcribed Image Text:In each part of this question, you are asked to give an example of something, and explain why it is an example. You may use all definitions, lemmas, theorems etc. from the lecture notes. (a) A sequence (an) such that, for every natural number , there exists a subsequence (an) of (an) converging to l. (You may use without proof that there exists a bijective function f: N→ NX N.)
(b) A sequence (fn) of functions on the interval [0, 1] that converges uniformly to the function
f(x) = x.
Transcribed Image Text:(b) A sequence (fn) of functions on the interval [0, 1] that converges uniformly to the function f(x) = x.
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Step 1: Define the sequence that satisfies the property.

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