You are here:

- Home
- Science
- Mathematics
- Number Theory
- Hypothetical Game

Advertisement

We play a hypothetical game. In round 1, I think of any 10-digit number and you try to guess that number. You are either correct in guessing that number or you are incorrect. In round 2, I think of any 10-digit number again and you try to guess that new number. You are either correct in guessing that new number or you are incorrect. We play an infinite number of rounds. Because we play an infinite number of rounds, I suggest that you are incorrect an infinite number of times, however, you are also correct an infinite number of times. In conclusion, you would be correct as many times as you would be incorrect.

The basis of my conclusion lies in the transitive property (although there may be other ways to illustrate it). If the number of correct answers are the same as the number of natural numbers and the number of incorrect answers are also the same as the number of natural numbers, then the number of incorrect answers and the number of correct answers are the same amount of elements. I can say that you would be correct 50% of the time.

Am I correct in my analysis? If not, please share with me where I made any errors.

Thanks,

Jimmy

Assuming you guess starting with 0 000 000 000 and end with 9 999 999 999, there are 10 billion possibilities. Only 1 of these is correct.

I can then split this table of guesses into two tables. The table of good ones will have only one right answer for every 9,999,999,999 answer is the other table.

If the two tables are chosen at random, there is a 50% chance of choosing the right table.

However, there is only 1 in 9,999,999,999.

When comparisons are made between two sets of infinity, a comparison like this is not looked at in this way since there aren't an infinite number of possibilities.

It could be said that this follows the law of large numbers. Consider a situation where you were allowed to choose a digit randomly each time. Even though there are an infinite number of choices, roughly one tenth will be of each number in the set. This can then be extended to 10 billion choices and the same conclusions be drawn.

- Add to this Answer
- Ask a Question

Rating(1-10) | Knowledgeability = 10 | Clarity of Response = 10 | Politeness = 10 |

Comment | Thank you. I appreciate the detail in your explanation. |

I can answer almost anything that is sent in. If I can't, I'll let you know, but I don't expect that to happen much.

I have known about number theory since the mid 80's. I have answered over 250 questions on Number Theory with this software. Altogether, I have answered over 8,500 questions in mathematics.**Publications**

You're looking at it ... I've answered over 8,500 quesitons in mathematics right here.
**Education/Credentials**

My credentials are an MS in Mathematics at Oregon State in 1986;
I received a BS in Mathematics at the same place in 1984.**Awards and Honors**

I graduated with honors in Mathematics when getting my BS degree and my MS degree.
**Past/Present Clients**

I have assisted many students in mathematics at OSU.
Perhaps I have assisted one of you're friends in math on a computer somewhere else,
but you don't even know... That would be late last night, perhaps with thousands of miles between us ...
Then again, if you're in Washington, so am I ...