On the second method, everyone gets a 1/500 chance of getting picked on the first draw, and if the first draw doesn’t pick anyone (which has a 92/500 chance of happening), then we repeat the process, again with everyone having the same chance of getting picked. Thus, the second method gives everyone an equal chance.

]]>We draw a single digit at a time.

First digit, one number 0 thru 4 would be drawn.

Second digit 0 thru 9, with one contingency: if a 4 is drawn on the first digit, the second is automatically a 0, then the third digit is drawn for a 0 thur 8.

If not, 0 thru 3 is drawn, then all ten numbers is drawn from, then third digit is drawn.

Third digit, is drawn from.

This is the fair method in which I believe in.

The opposing method is that if a 4 is drawn on the first digit, then all ten numbers are drawn from. If a 1 thru 9 is drawn, then both the 4 and the second number is thrown out, (because you are looking for a number from 1 to 408, only)

When a 4 is drawn on the first digit, a zero, must be drawn on the second for the drawing to continue. If not all number are thrown out.

Then you begin with the first digit again.

My argument is that is my number is 406, then I have a 9 in 10 chance that my number 4-hundred is eliminated after the first draw by the second draw, therefore, if I’m in the 4-hundreds, I have just as much of a chance to be eliminated on the second draw as the first. Thus my number has less of a chance to come up after a recurring draw. I am taking into accountability of the actual draw as a reduction of odds upon that draw. We’re only going to draw a single number through 408, not searching for the particular draw occurance.

Can anyone explain this in a better way???

]]>As a member of the “anti-platonist majority” (I think there were only two or three of us posting, hee!), I actually agree with what I think you’re saying. There’s a universal property of the usual natural numbers, a higher-order property if you like, which characterizes it up to isomorphism. It simply says that N is initial among pointed sets equipped with an endomorphism. That’s how I always think of N.

It’s a nice uniform definition which works for any topos or “category of sets”, and logical morphisms between toposes preserve natural number objects. So you really could say, in the sense of parametric polymorphism, there is only one true N! In their nice book on categorical logic, Lambek and Scott take this *sort of thing* as a possible resolution between Platonism and other philosophical positions, and that seems pretty reasonable to me.

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