Nine

What percentage of integers contain the digit 9 (at least once)?

Assuming you don't use leading zeroes, the chances that a given integer has a '9' in it is:

1 - (8/9)(9/10)^n

Where 'n' is the length of the integer in digits.

I guess you might take the limit of that as 'n' approaches infinity? But that would make it very close to "all of them" I think

What about this?

https://www.wolframalpha.com/input/?i=summation+from+n%3D1+to+infinity+of+%28%281-%288%2F9%29%289%2F10%29%5En%29%2F%2810%5En%29%29

Originally posted by forkedknight
Assuming you don't use leading zeroes, the chances that a given integer has a '9' in it is:

1 - (8/9)(9/10)^n

Where 'n' is the length of the integer in digits.

I guess you might take the limit of that as 'n' approaches infinity? But that would make it very close to "all of them" I think

Originally posted by forkedknight
Assuming you don't use leading zeroes, the chances that a given integer has a '9' in it is:

1 - (8/9)(9/10)^n

Where 'n' is the length of the integer in digits.

I guess you might take the limit of that as 'n' approaches infinity? But that would make it very close to "all of them" I think

Originally posted by AThousandYoung
If N = 1

1 - (8/9)(9/10) = 1 - (8/10) = 1/5

One fifth of all the one digit integers is not 9. Fail formula.

Originally posted by wolfgang59
Yes.
100% of the integers have at least one occurrence of the digit "9".

😀

All, except for an infinite number of them

But - and this is not a joke:

Among all integers there are exactly as many numbers with a nine in them as they are numbers without a nine in them. No approximately but exactly! Not as n reach infinity, but when n *is* infinity!

This is provable. Cantor showed us how.

Originally posted by FabianFnas
But - and this is not a joke:

Among all integers there are exactly as many numbers with a nine in them as they are numbers without a nine in them. No approximately but exactly! Not as n reach infinity, but when n *is* infinity!

This is provable. Cantor showed us how.

Originally posted by FabianFnas
But - and this is not a joke:

Among all integers there are exactly as many numbers with a nine in them as they are numbers without a nine in them. No approximately but exactly! Not as n reach infinity, but when n *is* infinity!

This is provable. Cantor showed us how.

Originally posted by forkedknight
Well the the answer should be 50%, and I don't think that's true...

Originally posted by FabianFnas
How much is 50% of infinity?