I do not have much time now but I was thinking maybe you can do this.Originally Posted byJameson

Then, it seems to me (I did not formally prove it) then,

are all solutions for each integer .

Thus,

Thus, since

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- Apr 6th 2006, 05:25 PM #1

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- Apr 6th 2006, 07:52 PM #2

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- Apr 7th 2006, 07:12 AM #3

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Let, us solve, for

We have,

Thus, all solutions for are,

Thus, we that, all solutions satisfies

Iff,

.

Note, cannot be zero or positive because it would violate the inequality .

Thus, all work.

Thus,

thus, length =.15

length=.015

length=.0015

and so on "ad infinitum" (I am so cool using latin phrases).

Thus, we have the total length of the solutions to be:

this is a regular infinite geometric series.

My point is that, we can "intuitively" think of probability as the length of the success (which are the solutions) divided by the total possibilities (which is the length of interval). Thus, the probability is .