What would happen if pi did appear in there completely?

Well my next point would be that if both pi and e were contained in that number entirely, then that means one of them has to contain the other, and that logic could be expanded to contain all irrational numbers... That just seems wrong.

As for "useful," I just meant mathematically relevant. I don't have any really strict idea of what the word should mean, just the opposite of what you meant when you said that .1234... was "utterly useless"

]]>Does that mean that both pi and e appear in there completely (I'm not just talking 3.14159265358979, I'm talking the whole thing) or does that only include finite works (like Shakespeare)?

What would happen if pi did appear in there completely?

And good point about it being useless, are there any predictable pattern irrationals that are useful?

What's your definition of useful? No matter what it is, as far as I know, no. But that's only as far as I know.

]]>And good point about it being useless, are there any predictable pattern irrationals that are useful?

]]>I vaguely remember reading somewhere that the number

.12345678910111213... (all the natural numbers just lumped together after the decimal place)

I don't know about any official name, but I call it the "number of everything". Translating it into binary and then ascii, every single play that Shakespeare wrote is in that number. Every single mathematical proof/definition/axiom is also in that number.

Cool, but utterly useless.

]]>.333333... = 1/3

But you can have a non-repeating but predictable number. I vaguely remember reading somewhere that the number

.12345678910111213... (all the natural numbers just lumped together after the decimal place)

has a name. Does anyone know what it is? Also I was thinking:

.2 1 2 11 2 111 2 1111 2 11111 2....(spaces added for emphasis)

Has to be irrational and predictable. (It's a 2 then one 1, then a 2 and two 1s then a 2 and three 1s, etc). Is anyone familiar with this? It's a little basic so it can't be new.

As I think more about it, there are defiantly an infinite amount of predictable irrationals. For example:

.112358132134.... (the Fibonacci sequence scrunched together)

Is a pretty obvious one, but you can make a Fibonacci sequence with any two starting values (4 and 5, or 1 and 3 for example) and because there are an infinite amount of natural numbers, that's an infinite amount of predictable irrational numbers.

So does anyone know a name for the predictable irrationals? Can anyone prove that they're transcendental (or not, I just assume they are)? Does anyone know of any cool ones?

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