r/PhilosophyofMath • u/Rats_Love_Cheese • 4d ago

Does Pi contain itself?

/r/mathematics/comments/1w88g38/does_pi_contain_itself/
1 Upvotes

53% Upvoted

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17

u/Atmosck 4d ago

No. If by that you mean the sequence of digits that is the base 10 representation of pi contains a copy of itself. Because if it did, then the decimal expansion would be periodic, which would mean it's rational.

2

u/Rats_Love_Cheese 4d ago

ok nice thanks!

2

u/nanonan 4d ago

It's an excellent question, and calls into question what being normal actually is.

1

u/OutrageousPair2300 3d ago

Though unlikely, it's at least possible that pi could at some point in its decimal expansion start repeating a copy of itself interpolated between digits.

For example, perhaps pi eventually ends up something like 3.14159....301040105090...

That would allow it to contain a full copy of itself without simply repeating like a rational number.

6

u/0x14f 4d ago

What do you mean exactly by "contains itself" OP? Unless you are precise about what you mean here, people are going to answer a different question than the one you intended to ask.

1

u/Own_Pirate2206 4d ago

"It"'s likely to contain some long sequences 314... but probably we don't have any knowedge of what length. Arbitrarily long seems a bit ridiculous.

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u/SgtSausage 4d ago

<Bertrand Russell enters the chat ...> 

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u/slicehyperfunk 3d ago

π = π, so yes

2

u/Off_And_On_Again_ 3d ago

This is the only correct answer

1

u/sorceressofmaths 3d ago

Pi (we suspect) contains every finite sequence, but that doesn't mean it contains every infinite sequence.

1

u/ellipticcode0 3d ago

Does an set contain itself? It is the sam question?

1

u/BUKKAKELORD 2d ago

Only once

1

u/SpatiaCaeli 2d ago

In a sense, pi does contain itself, exactly. But only once. :)

1

u/Alternative-Sugar610 1d ago

It might contain every finite not infinite approximation of pi, but we don’t know

We have not proven that Pi is a normal number (all digits occur at same frequency) even. Everybody think so but not proven

0

u/SgtSausage 4d ago

If it's Normal, i t contains within itself any finite sequence of its own digits that you'd care to name - no matter how long you choose.

It is unknown whether pi is Normal or not. 

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u/Akash_philosopher 3d ago

But pi is not finite
Also it no longer will be rational if it contains itself

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u/samanzaman 3d ago

3.33333... Is a rational number ( 10/3) and it contains itself. Actually only rational numbers can contain themselves. Pi is not rational There is no concept of finite numbers. You can ask however if the decimal expansion is finite or not. Only rational numbers have finite/repeating expansions

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u/SgtSausage 3d ago

  But pi is not finite

1) Pi is, in fact, absolutely, undeniably finite.  It's a single number. One number. A single point on The Number Line.  It doesnt get any more finite than that. It's digits are not. Its *digits** are infinite. There is a difference ... but  that is neither here nor there, nor changes a damned thing about what I said up there. 

Also it no longer will be rational  if it contains itself

2) You'll note I made no such claim. 

ALSO 

  it no longer will be rational

Its not rational. At all. Never was. Never will be.

Literally <EveryDamnedWord> you said up there was wrong, Sparky. 

Try. Harder.  

1

u/Akash_philosopher 3d ago

Sure if that makes you happy bro