OT: Are All Odd Numbers Prime?

Yes, with respect to even numbers.

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Google gave:

rec.puzzles Proof:

Consider these three statements:

1. There are three statements in this list.
2. Two of these statements are false.
3. All odd numbers are prime.

ObPuzzle: Show that statement 3 must be true.

Carl

Solution:

Statement 2 is false.

Proof (by the method of Harris):

Anyone who disagrees with me is a liar and has a vested interest in the validity of Statement 2.

two plus two equals four. except for very large values of two.

-- Many thanks,

Don Lancaster voice phone: (928)428-4073 Synergetics 3860 West First Street Box 809 Thatcher, AZ 85552 rss:

Please visit my GURU's LAIR web site at

pi = 3 for small circles ;-)

...Jim Thompson

-- | James E.Thompson, P.E. | mens | | Analog Innovations, Inc. | et | | Analog/Mixed-Signal ASIC's and Discrete Systems | manus | | Phoenix, Arizona Voice:(480)460-2350 | | | E-mail Address at Website Fax:(480)460-2142 | Brass Rat | |

I didn't expect relativistic addition of velocities in this thread! (*Nobody* expects relativistic addition of velocities in this thread!)

Also for larger circles, at least in the state of Indiana. By law.

Ah, yes, Indiana. They're right up there in the same league as Iowa who once denied adoption because a man had a beard and looked like a "hippy" ;-)

...Jim Thompson

Beards used to mean he-man. But we haven't had a bearded Presidnet since Benj. Harrison, or even a moustache since Taft.

Does Barbara Bush count?

Statement 3 is the only one not relating to the puzzle, thus 1 ansd 2 tie themselves up in a manner of speaking. Formally, #2 cannot be true because if it were true, #1 and #3 would not be true, according to the statement. But #1 *is* true, because there are three statements. Therefore, #1 must be true, which means #2 and #3 must be false; but for #2 to be false, two of the statements don't necessarily have to be false. Reductio ad absurdum or something like that, right?

Tim

That's almost there. #1 is true because there are three statements. Therefore #2 if true includes itself making it false, a contradiction, so #2 must be false which allows for one or zero statements false. If you consider the case of one false statement, it must be #2, making #3 true; and if you consider zero false statements, then #3 is true again. So #3 is true in either case- assuming no knowledge beyond the three statements as your universe.

ODDly speaking, numbers are PRIME for conversation like yours.

How about the "cheese sandwich theorem":

Conjecture: A cheese sandwich is better than complete happiness.

Proof: Nothing is better than complete happiness. A cheese sandwich is better than nothing. Therefore, a cheese sandwich is better than complete happiness.

mvh.,

David

Except that 'two of these statements are false', does not prevent all three of them from being false. If line #2, was 'Only two of these statements are false', the logic would change.

Best Wishes

Two or more statements false makes #2 false nonetheless, #2 can never be true because that assumption leads to contradiction. From this you have that NOT two statements are false. Since #1 is obviously true, you are left with one or zero false statements. Since #2 always has to be false, you cannot have zero false statements, which means there is exactly one false statement, #2.

There was a study published recently quantifying and explaining the observation that schizophrenics are significantly better than their sane counterparts at analytical reasoning, due in part to their "separation from reality" which apparently helps them avoid something called the context trap; inability to discern context is a characteristic of the disorder. Little puzzles such as this are best left to nutcases.

in

since

Q. How to get from prime numbers to Barbara Bush in 9 easy steps?

;D

In one of my calc classes years ago a good natured professor use to tell:

An engineer and a mathematician are given the task of boiling a pot of water in a room with a pot of water on one side and a stove on the other.

- The engineer says carry the pot of water to the stove, turn on the stove. - The mathematician says the same

Now they are given the same with the pot of water already on the stove...

- The engineer says turn on the stove. - The mathematician says carry the pot to the other side of the room and then you have reduced it to a previous problem.