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by phlip
Fri Sep 29, 2006 3:04 am UTC
Forum: Logic Puzzles
Topic: A very interesting Mathematical Paradox
Replies: 387
Views: 155351

I still say this is a definition of a certain language of strings, namely, the b -ary expansions (where b is the number of digits available to you). Well, yes. I did say "definition of a representation of a real number". I agree that the closure of Q under limits is a better definition of...
by phlip
Fri Sep 29, 2006 1:10 am UTC
Forum: Logic Puzzles
Topic: A very interesting Mathematical Paradox
Replies: 387
Views: 155351

...999 isn't infinite - it is very finite, it is exactly -1. I don't think limits come into it at all. 0.999... was never defined to me as a limit that converges, it was just said that the numbers repeat forever. You can't use operations defined only on real numbers in a proof to prove something is...
by phlip
Thu Sep 28, 2006 9:17 am UTC
Forum: Logic Puzzles
Topic: A very interesting Mathematical Paradox
Replies: 387
Views: 155351

The main problem is that the number ...999 does not exist in the set of real numbers. However, it may be possible to define a superset that works in the way you describe, and examine the consequences of performing algebra in that set. Let's, for the purposes of argument, define a superset of Z , suc...
by phlip
Wed Sep 27, 2006 1:01 pm UTC
Forum: Logic Puzzles
Topic: infinitely small triangle
Replies: 12
Views: 8691

What exactly are you trying to find out? That picture is, I think, a fractal , but other than that... I'm not sure what you're asking. Though, I can say that, in your drawing, each triangle's area is half that of the one before it, each triangle's edge length is √½ times that of the one befor...
by phlip
Wed Sep 27, 2006 9:39 am UTC
Forum: Logic Puzzles
Topic: Sum and Product Man
Replies: 27
Views: 15938

Sum knew that Product didn't know the answer before anything was said. That means that it can't be 2 and 6, because all Sum knows is that the sum is 8, which means that for all he knows it could be 3 and 5, which would imply Product knew the numbers (being the only factorisation of 15). But Sum knew...
by phlip
Wed Sep 27, 2006 9:24 am UTC
Forum: Logic Puzzles
Topic: Monty Hall Problem [solution discussion]
Replies: 68
Views: 25652

Two tactics I often use when people are confused by this problem: Just knocking down the paradox, without giving a solution: Probability says that if the result you're looking for is one result in a sample space of size n where the samples are all equivalent, the probability is 1/ n - the chance of ...
by phlip
Wed Sep 27, 2006 9:02 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0162: "Angular Momentum"
Replies: 103
Views: 58568

Um, if the girl was younger at the end of the night, surely that means that the night seemed shorter for her? If the guy's 12 hours older and the girl's 11.99999... hours older, then the guy saw the night as 12 hours long while the girl saw the night as that small amount shorter...
by phlip
Tue Sep 26, 2006 4:31 am UTC
Forum: Logic Puzzles
Topic: A very interesting Mathematical Paradox
Replies: 387
Views: 155351

1/3 is approximately equal to 0.33 - this is rounding.
1/3 is equal to 0.33333.... with an infinite number of 3s after the decimal point. There is no rounding involved, and the equality can be proven with limits and such.
by phlip
Mon Sep 25, 2006 9:43 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0162: "Angular Momentum"
Replies: 103
Views: 58568

Well, in answer to the caption, lessee... Assuming for now that there's no air resistance or anything like that... she just starts spinning at the start of the night, slowing the Earth, and then stops spinning at the end, speeding the Earth back up again. This is probably not even remotely like what...
by phlip
Mon Sep 25, 2006 6:25 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0162: "Angular Momentum"
Replies: 103
Views: 58568

This is incorrect? Each turn wouldn't rob the planet of angular momentum. Starting turning would rob the planet, but then the only thing that would allow additional turns to rob the planet of more angular momentum would be drag with the air (and this effect would also plateau). As long as you're tu...
by phlip
Mon Sep 25, 2006 5:43 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0162: "Angular Momentum"
Replies: 103
Views: 58568

Silly northern hemisphere and your silly backwards directions... everyone knows that you spin clockwise to slow the planet down. At least, in the real hemisphere. This is almost as mad as claiming Christmas belongs in the winter...
by phlip
Mon Sep 25, 2006 2:58 am UTC
Forum: Logic Puzzles
Topic: A very interesting Mathematical Paradox
Replies: 387
Views: 155351

1 - 0.999... < ε

What more is there to say?

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