Multiplying pi by 2 gives us another irrational number etc; but if we just wrote abunch of successive random digits (ad infinitum, somehow) are we creating an irrational number? can we create an irrational number or do they already all exist. Compare iron and nickle which produces stainless steel; was that created? iron and nickle always existed, but someone combined them and thus a new creation? If we wrote a combination of digits never before seen did we create that irrational number?

if we just wrote abunch of successive random digits (ad infinitum, somehow) are we creating an irrational number?
With probability 1, yes, since the real line is irrational almost everywhere (http://en.wikipedia.org/wiki/Almost_everywhere).

53876 x 10 8th power divided by 7 to the -8.576 multiplied by 10 to the 45th power divided by pi. Answer please? Does this answere your question?

No, its ducking it.

You cannot create an irrational number by generating random digits unless the algorithm goes on to infinity. It might also be provable that the algorithm is not random and that its result is a rational number.

No finite number of digits will produce an irrational number. I don't know exactly how to prove it this minute, but I believe that it is true that any finite number of digits can be expressed as a fraction. That makes it a rational number.

I don't know that you can "create" a number, but I guess you could be the first to "discover" or "define" it.

As Metakron suggested, the only requirement is that you have a deterministic algorithm that generates an infinite number of digits that never repeats itself. I added "deterministic" because I think that a truly random process (brownian motion, coin flipping, lava lamp) would not be appropriate because the number wouldn't be defined until it was completely generated... which would never happen.

Such an algorithm isn't hard to come up with. For example, here's one that defines an irrational number based on your name, "steponit".

First, convert the letters into numbers: STEPONIT = 19 20 5 16 15 14 9 20
Now repeat... but at each repitition, add one more of one number:

19 20 5 16 15 14 9 20 _ 19 19 20 5 16 15 14 9 20 _ 19 19 20 20 5 16 15 14 9 20 _ 19 19 20 20 5 5 16 15 14 9 20 ...

It's pretty simplistic, but it does the job. You could easily run it through a scrambler to make it look more random if you wanted to.

One trouble is that any pseudo-random algorithm is going to generate patterns of numbers that eventually repeat unless it cheats. The cheat would make the pseudo-random algorithm redundant. It would be to use pi or something like the square root of 2.

The cheat could be something as simple as placing incremental integers at regular intervals. After a billion digits, insert "1". After two billion, insert "2". After 347,635 billion, insert "347635".

I think that would work with much smaller intervals. That would make it easier to devise tests.

I don't even remember what kind, but there is some kind of irrational number that is patterned something like that, so its pattern changes, like the interval between repeated digits keeps increasing in a predictable pattern. Two such numbers can be added to each other to make a rational number.

can we create an irrational number or do they already all exist.

You can create an irration number anytime you want. However, there is NO way you can find a way to list them all. Trying to list them all show shows you can create a new irrational number that is different from all the irrational numbers.

No finite number of digits will produce an irrational number. I don't know exactly how to prove it this minute, but I believe that it is true that any finite number of digits can be expressed as a fraction. That makes it a rational number.n is a number with N digits so n = n*10^N/10^N. Since 10^N is an integer and n*10^N is an integer n is rational.

-Dale

I think that would work with much smaller intervals. That would make it easier to devise tests.
Yes, it would work with any interval at all. Even zero:

0.1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30...

I don't even remember what kind, but there is some kind of irrational number that is patterned something like that, so its pattern changes, like the interval between repeated digits keeps increasing in a predictable pattern. Two such numbers can be added to each other to make a rational number.
Yes, there is any number of simple deterministic ways to make irrational numbers of that kind.

I don't know exactly how to prove it this minute, but I believe that it is true that any finite number of digits can be expressed as a fraction. That makes it a rational number.I don't know how to state it in the language of a math book, but here's how you do it.

Let X be your number, expressed in decimal notation.
For the sake of brevity, assume 1 > X > 0. It should be obvious how to extend this to values of X > 1.
Let D be the number of decimal digits. By definition, D is finite.
Let A = 10 ^ D. This creates an integer, a power of ten with the same number of zeros as the decimal places in X.
Let B = X * A. This shifts the decimal point in A exactly to the right of the last non-zero digit, creating an integer.
Let F be a fraction whose numerator is the integer B and whose denominator is the integer A.

F = B / A,
therefore F = (X * A) / A,
therefore F = X.

Q.E.D.

BTW... The methods described above for creating an irrational number do not generate random numbers because they have been described right here as formulas. This proves that you do not have to have a reliable random number generator to build an irrational number. It can be done by algorithm, just like fractional exponentiation.

Speaking of which, how do you prove that a number like 2 ^ .5 is irrational?

I barely have any idea how to prove that the pattern does not repeat itself. I would have to get back to you on that and that's not a high priority, actually. Maybe someone has already done it somewhere.

One approach to the idea is to show that there is no number with anything to the right of the decimal point that multiplied by itself a whole number of times will produce a whole number. I don't know that this is true in all number bases, either.

Speaking of which, how do you prove that a number like 2 ^ .5 is irrational?
This was apparently proved geometrically by Hipassus (http://scienceworld.wolfram.com/biography/Hippasus.html) around 500 BC.

The usual way is a proof by contradiction.
Begin with the assumption that two integers P and Q exist such that:
P²/Q² = 2, and
P and Q have no common factors (specifically, that at least one is odd),
then show that this leads to a logical inconsistency, eg that both P and Q are even.

That won't work for odd numbers.