Recent content by JeffJo

We need only two sets: ##N##, the set of all natural numbers, as defined by the Axiom of Infinity. ##C = P(N)##, the power set of ##N##. Each element c of ##C## is a subset of ##N##. But note that we can represent c as an indexed string, where the nth character of c is a 1 if n is in the...

The one Cantor published in the 1890 paper Uber ein elementare Frage der Mannigfaltigkeitslehre. Translation at http://www.logicmuseum.com/cantor/diagarg.htm . It actually was not the theorem that paper was written for. It was an example, much like you might show a (3,4,5) right triangle before...

Yes, I know some of this repeats Perok, Some doesn't. (A) If such a set is limited to finite-length sequences, it is countable. (B) If they are infinite-length, it is uncountable. Cantor's Diagonal Argument. The real one, not the one taught in introductory courses, which is better remembered...

A horse walks into a bar. The bartender says to it: "Hey, haven't you been in here every day this week? Are you some kind of a lush or something?" The horse replies "I don't think I am," and immediately disappears in a puff of smoke. You see, a famous philosopher once explained that his own...

Not sure what you mean. None of the previous 84 comments have even touched on what I said was "clearly true." It was about how a different formulation of the problem corresponds to the original. I keep trying to get discussion to happen, but the only comments I have gotten are about incidental...

And again, "I/You/We/They agree that the break-even betting odds is 1/3" is a conclusion. About both the betting odds, and who agrees. I've never had anybody agree or disagree, whether thirder, halfer, or on-the-fencer. I thought this forum might evoke more direct discussion than some others...

And again, I agree with your conclusion that confidence should be 1/3. But I disagree with using any argument based on betting, since there are those who will disagree with how the betting should proceed. Whether or not they post here, their reasoning appears to be similar to arguments that are...

If, over the entire procedure, you risk losing only $1 on either result, and win only $1 on if you are right on either result, the break-even odds are 1:1 (the probabilities are 1/2). If you risk losing only $1 on heads, but $2 on tails? And win only $1 on if you are right on heads, but $2 on...

Dale, I agree 100% with your conclusions. But not with your reasons. The issue with the betting argument, is whether the entire procedure involves exactly one bet, or one-or-two bets, depending on the coin. Again, I agree with the result that one-or-two bets is correct, but you can't divorce...

Again, in the two-coin version, there is one probability space (I'll call it PS1) that applies to when the decision is made to wake you. (Note: I am deliberately using "you" instead of "SB" to distinguish my version.) The sample space contains the four outcomes {HH, HT, TH, TT}. The probability...

You are confusing knowledge about how the random state is created and changed, with knowledge about what that state is at a moment in time. We do understand that she had full knowledge on Sunday Night about the eventuality of being awake. That is not the knowledge that allows one to update the...

It is my opinion that halfers want "credence" to have a different meaning than "probability," so that they can dismiss arguments that use probability theory.

This opinion is based on the misconception that SB "receives no (new) information" by being wakened. Yet I have seen no definition of what halfers who say this think "new information" means, even from the ones who keep demanding that I supply one. They have said that because she knew she would...

From Wolfram's Mathworld: "A general prism is a polyhedron possessing two congruent polygonal faces and with all remaining faces parallelograms (Kern and Bland 1948, p. 28; left figure)." I don't want to be as pedantic as some of these responses. This was about color, and why you should say...

I didn't say it wasn't a light-deflecting device. I said the way the effect is formed is not due to what people think of as the prism effect.