(4t6) 46+62 2+46-160 9. 16 4. Consider the following infinite collection of real numbers between 0 and 1. 4676 6= -2+ 2 V5,-2-215 0:1212212221222212222212 : :: 0:0202030405060708091011 ::: 0:2337111317192329313741 0:3574111315171921232527 0:2468501214161820222426 : : : 0:5000060000000000000000 : :: 0:3333337333333333333333 : :: 0:1248163864128256512102 : :: 62 0: 2,3, 4,f,6,7,8 2.47 もこ- = Use only the digits 1 and 3 to create a number, between 0 and 1, with an infinitely long decimal expansion that is NOT on the list. Notice that the list goes "on and on". Explicitly describe vour tochnique for creating the new number and explain how you know your number will never appear on the list.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 73E
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From the book: heart of mathematics 4th edition.

(4t6)
46+62
2+46-160
9.
16
4.
Consider the following infinite collection of real numbers between 0 and 1.
4676
6= -2+ 2 V5,-2-215
0:1212212221222212222212 : ::
0:0202030405060708091011 :::
0:2337111317192329313741
0:3574111315171921232527
0:2468501214161820222426 : : :
0:5000060000000000000000 : ::
0:3333337333333333333333 : ::
0:1248163864128256512102 : ::
62
0: 2,3, 4,f,6,7,8
2.47
もこ-
=
Use only the digits 1 and 3 to create a number, between 0 and 1, with an infinitely long decimal
expansion that is NOT on the list. Notice that the list goes "on and on". Explicitly describe vour
tochnique for creating the new number and explain how you know your number will never
appear on the list.
Transcribed Image Text:(4t6) 46+62 2+46-160 9. 16 4. Consider the following infinite collection of real numbers between 0 and 1. 4676 6= -2+ 2 V5,-2-215 0:1212212221222212222212 : :: 0:0202030405060708091011 ::: 0:2337111317192329313741 0:3574111315171921232527 0:2468501214161820222426 : : : 0:5000060000000000000000 : :: 0:3333337333333333333333 : :: 0:1248163864128256512102 : :: 62 0: 2,3, 4,f,6,7,8 2.47 もこ- = Use only the digits 1 and 3 to create a number, between 0 and 1, with an infinitely long decimal expansion that is NOT on the list. Notice that the list goes "on and on". Explicitly describe vour tochnique for creating the new number and explain how you know your number will never appear on the list.
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