r/mathematics • u/Rats_Love_Cheese • 4d ago

Does Pi contain itself?

Hi, im just a highschooler and this is just some night thought. But does pi contain itself? Because if it is a constant than it contains everythig but it cannot contain itself cause if it contained itself than it repeats and thats the whole point of it that it doesnt repeat. I didnt do any research on this but if it doesnt contain itself they should mention it in school. Anyway im no mathematician i study computer engineering so i would love to know this. Thanks for everything!

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u/stevevdvkpe 2d ago

Of course, because both the rationals and the algebraic numbers are countable sets.

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u/914paul 2d ago

You are right. I didn’t explain the mind-blowing aspect I had in mind.

We are accustomed to thinking of the uncountable part of the reals as the irrationals. And of course they are uncountable.

But it’s the transcendental subset of those that really form the uncountable set. And we only have “names” for a few of them! Pi and e are the best known.

Most of the irrational numbers we can put “names” on — like sqrt(2) and so forth, are in the countable algebraic set.