Define a digit to be an element of the set (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) Show that any real number x & [0, 1] can be represented as x = 0.a₂a₂a.....for some sequence of digits {a} n=1
Define a digit to be an element of the set (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) Show that any real number x & [0, 1] can be represented as x = 0.a₂a₂a.....for some sequence of digits {a} n=1
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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![**Topic: Representation of Real Numbers in Decimal Form**
Define a digit to be an element of the set \(\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}\).
Show that any real number \(x \in [0, 1]\) can be represented as \(x = 0.a_1a_2a_3 \ldots\) for some sequence of digits \((a_n)_{n=1}^\infty\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F37e8ed93-7bef-4409-89ed-52264f64a27e%2F69c1669e-7ddf-4755-964b-c79ec92468b7%2Fcxyqc5e_processed.png&w=3840&q=75)
Transcribed Image Text:**Topic: Representation of Real Numbers in Decimal Form**
Define a digit to be an element of the set \(\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}\).
Show that any real number \(x \in [0, 1]\) can be represented as \(x = 0.a_1a_2a_3 \ldots\) for some sequence of digits \((a_n)_{n=1}^\infty\).
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