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Terry is writing a book that he's publishing in several universes (this is distinct from several versions of Terry publishing in their respective universes). He needs to identify which universe he came from, so the other versions of himself don't get credit for HIS hard work.

Generally, universes are numbered anywhere from 0 to 1. This means that most universes can be represented by an irrational number.

Is there anyway practically to identify which universe you are in, when you have limited sheets of paper and limited font size?

In other words, can a given irrational number be written in finite terms? If not, is there some way around this?

Edit: The numbers 0 - 1 are inherent. Terry knows the number of his universe, and his target audience knows their own. The numbers are uncountably infinite.

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    $\begingroup$ This is really a math question, not a woldbuilding question, but I can give two hints. First, there's multiple sizes of infinity in mathematics. If it is a countable infinity, you can map his universe to an integer. If its an uncountable infinity, you cannot. Your reference to irrational numbers suggests the set of universes is uncountable. That being said, the answer to any question involving infinity and practical applications is almost always "no." $\endgroup$
    – Cort Ammon
    Commented Sep 30, 2016 at 3:42
  • $\begingroup$ Also, I highly recommend VSauce's video, How to Count Past Infinity. It is the only layman accessible description of the mathematical concept of infinity that I have ever found. (read: everything I know about infinity I either learned from his video, or wish I'd learned from his video instead of learning the hard way) $\endgroup$
    – Cort Ammon
    Commented Sep 30, 2016 at 3:48
  • $\begingroup$ The easiest way would be to include a picture of himself, as the Terry from the Moustache-Universe and the Terry from the Cowboy-hat-Universe are quite easily to distinguish $\endgroup$
    – dot_Sp0T
    Commented Sep 30, 2016 at 4:04
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    $\begingroup$ As for the actual question, I don't think it's about maths really. I mean Terry could devise any system he'd wanted to number the universes. He could number them 1/N (note that those aren't irrational numbers), or $\pi/4N$ is it really have to be irrational. And N can indicate the Nth universe he visited. But the problem is to get that numbering (multi-)universally recognised... Especially if he'd rather avoid disputes with himself in those other universes. $\endgroup$
    – clem steredenn
    Commented Sep 30, 2016 at 8:18
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    $\begingroup$ Is he publishing to all universes or a finite subset? If it's a subset, couldn't he define himself with a unique pen name within that domain of universes? That way everyone knows it's him, but without even needing to buy into the parallel universes part. (and is everyone aware of the alternate universes?) $\endgroup$
    – Tezra
    Commented Sep 30, 2016 at 17:12

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Wait a bit who numbered the universes? Basically identifying which universe you're in, will only be a matter of practical convenience.

Assuming you have a mechanism for transporting persons from any one universe to another, it's only a matter of establishing a beacon or a marker to indicate any given universe. Your home universe will have its own specific beacon.

Provided there is a way of navigating between beacons and universes, then intercosmological travellers will know they have left their home universe and arrived in given universe whatever. Where "whatever" can be any identifier you care to use.

This can be a number or a name of your choice or it might be based on a distinguishing feature of that universe, for example, this is the universe where skies are green instead of blue or people have orange hair and purple skins.

Sorry whoever gave each universe an irrational number may have been a great mathematician, but he was a lousy navigator. Finding your way about among even an infinite set of universes is a problem of navigation not mathematics.

So how can someone identify which universe they came from? They will name it their home universe and look for where their home beacon is located.

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Terry needs to stay at home, or he is are lost forever

Seriously, he does not want to leave your "home" universe because unless he has the equivalent of a string attached to him that he can follow back, he cannot get back.

The core of your question:

In other words, can a given irrational number be written in finite terms? If not, is there some way around this?

As Cort Ammon said, if it is a countable number of universes, then you can. If it is not a countable number of universes — and since you mention irrational numbers, that is the case — then no, then you cannot do it.

The reason is that Terry cannot write down the number that identifies his Universe. Irrational numbers go on forever, so there is no "note" big enough to fit the identifier.

"Ok" says Terry, I'll just get a near approximation of the number, I do not need to write down the whole thing". So he writes down "his" universe's number to a million significant digits and goes on his multi-verse book tour. Then he tries to go home...

...only to find an infinite amount of universes that have the exact same million of significant digits as his own.

Infinity is a somewhat mind-breaking concept, and there is no way you can cheat it because we live in a finite universe. So unless Terry is lucky enough to live in a universe that is identified by a rational number or any of the great constants, like $\pi$ or $e$, then he really should stay at home or he will never find his way back.

And this is not even beginning to explore what it actually means to have an infinite amount of universes. Things start to get silly really fast...

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