possible ?

Question

is it even remotely possible that pi is not in fact an infinite number?

Answer 1

from a mathematical point of view it is possible that pi is not an infinite number because we have no real way of telling if it is infinite or not. Coming from a sort of philosophical point of view many things these days that are happening seem to be impossible, suggesting that everything is possible. From many points of view, the answer is that it very possible.

Answer 2

Pi is finite. It is between 3 and 4. That makes it a finite number.

However, its decimal expansion is infinite. But then, so is the decimal expansion of 1/3. On the other hand, pi has an infinite expansion no matter what base you use. Why? Because it is irrational. That means it cannot be written as a fraction p/q with both p and q whole numbers. Since every number with a finite expansion *can* be written in this way, pi has an infinite expansion.

As Eulercrosser mentioned, pi is even worse than simply being irrational. It is actually transcendental (meaning it is not the root of any polynomial with whole number coefficients). So, for example, sqrt(2) is irrational, but it solves the equation x^2 -2=0. Pi can't even solve an equation like that.

Answer 3

Eulercrosser is correct.

Irrational number are numbers that cannot be written as a fraction of two integers. Irrational numbers also always have an infinate number of non repeating decimals. If a number contains a finit number of decimals, then it can always be written as a fraction of integers. pi has been proven to be an irrational number, along with the square root of any prime number, and e. The opposite of an irrational number is a rational number. Rational numbers can always be written as a fraction of two integers, and always have a limited number of digits or the digits start to repeat.

You might be wondering how this would be possible to prove. If you listed the digits, and reached the end, you could show it was rational, but if there was an infinate number of digits you could never get to the end, which means that you could never show it was infinately.

However, there is a way to prove it's digits go on forever. This proof could go somthing like this. Let a and b = integers. Since a / b can't have more than b-1 repeating digits (in any base), all you have to do is prove that a / b can never equal pi.

The proof that pi is irrational is rather complicated. I've listed two proofs in my sources. Any irrational number is also irrational in every base.

There is absolutely no possibility that pi is a rational number. It has been proven to be irrational.

Answer 4

Is it possible, yes, but the truth will never be known until we actually reach the last digit of pi. As for the gentleman above who believes he has reached the final digit of pi in binary, do you realize how insane that proposal is? Assuming pi extended a million places beyond the decimal point, which it doesn't, it goes further, the binary equivalent would be 5 times that size and an absolute waste of time. Furthermore I would like to know the numbers you are using to attempt to find this answer, their binary equivalents, and what super computer you happen to have at home...

Answer 5

I will first assume that you are talking about the fact that π can't be written as a number with finitely many digits. First of all, this is the same thing as saying that π is irrational.
To all the people that have said "anything is possible," that's not true, and in this case, it still isn't.

My only guess to people assuming that π cannot be proven to not have a finite decimal expansion (π's irrationality), is because they assume that to prove it can't, you have to find it's infinite decimal expansion. This is something that can't be done, of course.

But that is NOT the method to proving π's irrationality.

The method is a proof by contradiction (at least the one that I know of). It proves that if π is a rational number then there is an integer between 0 and 1. Since there is no integer between 0 and 1, π thus cannot be rational, and must be irrational.

Actually, π is more than irrational, it is actually "transcendental." This means that there does not exist a polynomial (of finite degree) with rational number coefficients, such that π a root of this polynomial. This is much stronger than saying π is irrational, because if π was rational, then x-π would be a polynomial (of finite degree) with rational number coefficients, such that π is a root of the polynomial.

I have included below a link to a proof of the irrationality of π. To be honest, you may not understand it, but to the person above me that says "until proven impossible, it remains in the realm of 'the possible.'"(which is a true statement);
It no longer remains in the realm of "the possible," because we have proven it to be impossible.

Answer 6

First, pi is not infinite... it is irrational. Now, consider this... who really cares where pi ends. Scientists typically use 3.142. Mathematicians typically use 3.14159. No one really uses the accurate pi measurement anyway. The only people I have found interested in the terminus of pi are those Mathematicians or Computer Scientists trying to get their PhD.

In short, will we find it is finite? No, not as long as someone wants their PhD. Otherwise, pi has been resolved as far as anyone is concerned for hundreds of years.

Answer 7

No
Search Pi to 40 Million DigitsFind strings of digits in the first 50000000 digits of Pi.
at
www.angio.net/pi/piquery

Answer 8

Absolutely. Anything is possible in a world of infinite possibilities.

Answer 9

Technically it's not infinite, it's between 3 and 4. It's quite small actually. ;)

Answer 10

Until proven impossible, it remains in the realm of "the possible." And to prove it impossible, all it would take it to connect unto a sequence, however long, of repeating numbers, that are (of course) non-terminal.