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→Pi contains every other number?: some fun with finding strings in π
Thank you for your patience! --[[User:AugustO|AugustO]] ([[User talk:AugustO|talk]]) 01:38, July 30, 2021 (EDT)
Thank you for your patience! --[[User:AugustO|AugustO]] ([[User talk:AugustO|talk]]) 01:38, July 30, 2021 (EDT)
:Yes, that's right. The aspect of [[infinity]] illustrated by the observation that [[pi]] contains pi is similar to several of the [[miracle]]s and [[parable]]s in the [[New Testament]].--[[User:Aschlafly|Andy Schlafly]] ([[User talk:Aschlafly|talk]]) 13:10, July 30, 2021 (EDT)
:Yes, that's right. The aspect of [[infinity]] illustrated by the observation that [[pi]] contains pi is similar to several of the [[miracle]]s and [[parable]]s in the [[New Testament]].--[[User:Aschlafly|Andy Schlafly]] ([[User talk:Aschlafly|talk]]) 13:10, July 30, 2021 (EDT)
From your "induction proof", I got the impression that you were looking for increasingly long strings resembling the leading digits of π - I looked the first few up for you:
{|
|'''x<sub>9</sub>'''x<sub>10</sub>||=||'''3'''5
|-
|'''x<sub>137</sub>x<sub>138</sub>'''x<sub>139</sub>||=||'''31'''7
|-
|'''x<sub>2120</sub>x<sub>2121</sub>x<sub>2122</sub>'''x<sub>2123</sub>||=||'''314'''2
|-
|'''x<sub>3496</sub>x<sub>3497</sub>x<sub>3498</sub>x<sub>3499</sub>'''x<sub>3450</sub>||=||'''3141'''2
|-
|'''x<sub>88008</sub>x<sub>88009</sub>x<sub>88010</sub>x<sub>88011</sub>x<sub>88012</sub>'''x<sub>88013</sub>||=||'''31415'''1
|-
|'''x<sub>146451</sub>x<sub>146452</sub>x<sub>146453</sub>x<sub>146454</sub>x<sub>146455</sub>x<sub>146456</sub>x<sub>146457</sub>'''x<sub>146458</sub>||=||'''314159'''7
|-
|'''x<sub>25198140</sub>x<sub>25198141</sub>x<sub>25198142</sub>x<sub>25198143</sub>x<sub>25198144</sub>x<sub>25198145</sub>x<sub>25198146</sub>x<sub>251981407</sub>'''x<sub>25198148</sub>||=||'''3141592'''1
|}
But this does not imply that the whole digital representation of π can be found as a consecutive string in π again. In fact, that is impossible.
Yours statement is like saying that as 1, 11, 111, 1111, 11.111, 111.111 and so on are natural numbers, an infinite string of 1s is a natural number, too: And I hope we can agree that this is a false statement.
--[[User:AugustO|AugustO]] ([[User talk:AugustO|talk]]) 17:41, July 30, 2021 (EDT)