Does Pi contain my phone number.

[Adalbertus]

For all you pi freaks, there is a link to a pi page http://mathforum.com/dr.math/faq/faq.pi.html
You'll find a proof for the irrationality of pi, based on showing that there are no integers p and q such that pi = p/q. It requires some calculus (integration, differentiation). I won't reproduce it here, because it requires more prerequisites and is less interesting than the infinity things.

I didn't find any proof on the web regarding "any finite sequence of digits can be found in pi". If it exists, it is probably rather difficult. Note that it is not equivalent to normality, it is a weaker statement (being a corollary of normality). Any mathematician here knows about this?

I'm a bit puzzled now, because I thought it already had been shown.

Just like I can show you that it's probable that any number you show me is irrational...

Krazy Horse, you proof will need the assumption that SnowFire has no information about what is a rational and irrational number ...

All odd numbers are prime

[KrazyHorse]

Any mathematician here knows about this?

I'm pretty damn certain it hasn't been shown. The proof for that and normality would probably fall together...

Krazy Horse, you proof will need the assumption that SnowFire has no information about what is a rational and irrational number ...

That's the point. Snowfire said that Pi was probably normal, for the same reason that I can say "x" is probably irrational for any "x"

All odd numbers are prime

Actually, very few odd numbers are prime. As you can imagine, the density of primes --> 0 as your sample size grows larger...

[Skanky Burns]

All odd numbers are prime

15? 21?

[KrazyHorse]

There's a 62.5% chance that 15 is prime, and a 63.636% chance that 21 is prime.

[Skanky Burns]

[Adalbertus]

At least someone has understood that I wanted to hint to an old joke. How to show by induction that all odd numbers are prime:

Mathematician:
1 - ok, doesn't count really
3 - prime
5 - prime
7 - prime
therefore shown by induction that all odd numbers are prime.

Physicist:1 - ok, doesn't count really
3 - prime
5 - prime
7 - prime
9 - error of measurement
11- prime
therefore shown by induction that all odd numbers are prime.

Economist:
1 - ok, doesn't count really
3 - prime
5 - prime
7 - prime
9 - prime
11- prime
therefore shown by induction that all odd numbers are prime.

[Skanky Burns]

Math jokes aren't really my thing.

Putting it that way though:

[Guest]

Lots of good point of course ure right KrazyH
and i was wrong about that being true for every irrationnal number
your 0.010010001 w (in decimal) hich IS Transcendental by the way does not contain a 7 of course
i checked about this today
for pi though it is it just cant be generalized to all irrational like i thought.
What aldbertus said was right
You can prove pi irrational and even transcendental (i can dig up the one on the irrationality somewhere)
And like he said, for infinite sets, the way to check which set is bigger is if you can make a bijection beetween them.
Its a know property of infinite sets that they can have the same cardinalty as a subset of themselves (integers and even numbers come to mind).

[Caesar the Great]

If you think a bit over it you will make the stunning discovery that there are as many even numbers as integers (see below for something even stranger). This seems to be odd at first, but there is no better way to define the "number of elements" for infinite sets.

wouldn't that mean odd integers don't exist? which would mean 2 is the only prime number? hmm....

[Adalbertus]

wouldn't that mean odd integers don't exist? which would mean 2 is the only prime number? hmm....

No. Al LulThyme said, for infinite sets, a real subset can have the same cardinality. This is sensible, and most fun to understand the thing with the infinitely big hotel.
Atm I think that the better exercises are:
1) A bus with n guests arrives
2) A bus with an infinite (#N) number of guests arrives
3) An #N buses with #N guests each arrive.
You all get them into the hotel, even if it is full before the first bus arrives.

Again to integers: The set of all integers, all rational numbers, all even, and all odd integers, and the set of all primes each have the same cardinality. Even if some of them are subsets of some other.

If this seems all too strange for you: The mathematicians themselves didn't really understand this until about 1880 (mostly work of G. Cantor).

[KrazyHorse]

for pi though it is it just cant be generalized to all irrational like i thought

I'm pretty sure that nobody's ever proved it true even for Pi. It certainly smells like it's true, but we aren't certain...

[SnowFire]

Yeah yeah, I meant normal. It seems highly unlikely that pi is rational, being that if it is, we have a whole lot of math to rewrite.

Don't forget other weird possibilities as well, folks: maybe pi is normal to all bases except base 7, base 320, and base 3 trillion.

Adal: That Economist version I've usually seen tagged as "English major," but indeed, 'tis always amusing.

KrazyHorse: Probable? Nay, certain, if I'm being fair and picking from the reals. But yeah, it still stands as just probable for pi.

[Adalbertus]

It seems highly unlikely that pi is rational

I hope you meant "not normal" instead of "rational". When you follow the link I provided a bit above and surf a bit you'll find a proof that pi is irrational.

[Seeker]

"The proper word is frequency. Conner's phone number appears more frequently than your number.

Please note that both numbers appear an infinite number of times inside Pi."

I don't understand how a a pattern of numbers which repeats an infinite number of times can be said to appear 'more frequently' than another pattern which ALSO appears infinetly.

How many times does pattern A appear in pi? Answer: Infinitely.

How many times does pattern B appear? Infinitely.

On what basis do you say that one is more 'frequent'?

If you have a number like this: 0.1111111111.., but every millionth digit is a number 2-9, and the number was infinite, why is it that '1' is considered more frequent? Doesn't 1 appear at the same frequency, i.e. infinitely?

[KrazyHorse]

Originally posted by Adalbertus

I hope you meant "not normal" instead of "rational". When you follow the link I provided a bit above and surf a bit you'll find a proof that pi is irrational.

I think that was his point...