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question on pi within pi
:Your [[infinity denial]] is illogical. I urge you to welcome and embrace [[infinity]] (yes, by implication [[eternity]]), and use it for your own benefit. I want you to realize all the happiness and glory it provides.--[[User:Aschlafly|Andy Schlafly]] ([[User talk:Aschlafly|talk]]) 16:52, August 2, 2021 (EDT)
:Your [[infinity denial]] is illogical. I urge you to welcome and embrace [[infinity]] (yes, by implication [[eternity]]), and use it for your own benefit. I want you to realize all the happiness and glory it provides.--[[User:Aschlafly|Andy Schlafly]] ([[User talk:Aschlafly|talk]]) 16:52, August 2, 2021 (EDT)
::Are you still talking about mathematics? --[[User:AugustO|AugustO]] ([[User talk:AugustO|talk]]) 17:00, August 2, 2021 (EDT)
::Are you still talking about mathematics? --[[User:AugustO|AugustO]] ([[User talk:AugustO|talk]]) 17:00, August 2, 2021 (EDT)
"assume pi contains pi as n significant digits in a finite representation of pi. Pi must also contain pi as n+1 significant digits" - so pi (assuming it's a normal number, as Augusto said) contains any truncated version of pi of any finite length (no matter how many zillions of digits). An infinite number of each truncation. It would also imply that any finite string of digits of pi would be replicated an infinite number of times elsewhere in the string of digits.
"as the number of digits of pi is stretched to infinity." Is it necessary that the pi within pi start at a digit infinitely far from the first digit? That would get around the periodicity issue.
The mathstack discussion:
https://math.stackexchange.com/questions/1608060/does-pi-contain-itself
I kind of like the idea of two points on a line being infinitely far from each other, with a third halfway in between, but I don't think that's part of the current standard set of axioms.
We're ignoring the decimal point, right? There's only one of those. Anyway, this is a pretty interesting discussion.
===Linking to this section from the article===
===Linking to this section from the article===
Andy, do you really think that it is a good idea to link to the above section '''on a talk-page''' from the main article on [[pi|π]]? And please, read the discussion! (ups, that was the second sentence of this paragraph - you probably already started skipping...) --[[User:AugustO|AugustO]] ([[User talk:AugustO|talk]]) 05:23, August 3, 2021 (EDT)
Andy, do you really think that it is a good idea to link to the above section '''on a talk-page''' from the main article on [[pi|π]]? And please, read the discussion! (ups, that was the second sentence of this paragraph - you probably already started skipping...) --[[User:AugustO|AugustO]] ([[User talk:AugustO|talk]]) 05:23, August 3, 2021 (EDT)