4 ms·

Well, there IS an integer that contains all the digits of Pi 3141592...

• hugh3 16y ago
  No, that "integer" would need to have an infinite number of digits, and no integer has an infinite number of digits.
  • asmithmd1 16y ago
    So you are saying that their is a largest integer with a finite number of digits? Lets call that integer N, wouldn't 10*N have one more digit than N?
    • crazyjimbo 16y ago
      Integers can have an arbitrarily large but finite number of digits. They cannot have an infinite number of digits. There is a big difference.
      • asmithmd1 16y ago
        I guess we are in the realm of cardinality of infinity which I don't quite get. I would think an infinitely big integer would have an infinite number of digits. So you are saying: log(infinity) < infinity
        • hugh3 16y ago
          Once again, there is no such thing as an infinitely big integer. You seem to be having difficulty with the fact that: 1. There are an infinite number of integers, but 2. Every integer is finite Start counting 1,2,3,4... Do you ever get to the end? No, this proves that there are infinitely many integers. But do you ever get to an infinite number? No, you'll stay in the set of finite integers forever.
    • hugh3 16y ago
      No, there is no largest integer with a finite number of digits. There are infinitely many integers, but every integer is finite.
    • jaf656s 16y ago
      You are confused: yes there are infinite integers, but every single integer has a finite number of digits. Edit: (Several people have said the same thing so maybe I can add something else) I think another point of confusion might be the difference between "arbitrarily long" and "infinitely long". The number pi is infinitely long, a single integer can be arbitrarily long. What's the difference? Pi has infinite digits. It is an irrational number. We can never "see" all the digits of pi, because no matter how far out we go there are always more digits. With an integer, this isn't the case. There are infinite integers, but this property is defined on the set, not on any single element in the set of integers. Every integer (a single element in the set of integers) is finite. All of them, no matter what. They all have an end. That said, what "arbitrarily long" means is that for any length you choose, there are integers that long (or longer). Say we choose a length 5, then 10000, 10001, 10002, ... all have length 5 or greater, but every one of them has an exact length. It just happens to be greater than 5. You can do this for any length: 1000, 10^1000, whatever. Anything. Choose any number as big as you can even imagine. Try to imagine numbers bigger than anything you can even imagine. There are integers that long, and infinitely more integers longer than that. But every single one of them has an exact, finite length.
      • mzl 16y ago
        This is all true, assuming one uses a standard model for the integers. Non-standard models[1] are more interesting, but I'm not sure if one could say anything about the number of digits of a non-standard number. [1] http://en.wikipedia.org/wiki/Non-standard_model_of_arithmetic http://en.wikipedia.org/wiki/Non-standard_model_of_arithmeti...
• WilliamLP 16y ago
  > Well, there IS an integer that contains all the digits of Pi 1234567890 does:)