On 04/03/10 14:38, Steve Holden wrote: <cut>
If you think you will persuade a crackpot to drop his lunacy by logical argument you are clearly an optimist of the first water. But since I like a challenge (and bearing in mind this is OT so I don't claim to be an expert) you might try first of all persuading him to agree to the commutativity of multiplication (i.e. x * y == y * x for any x and y). If he agrees to that, then get him to agree that x * 1 == x for any x. If he agrees to that, then set x = 1/2 and see if he'll agree that 1/2 * 1 == 1/2. If he does, then surely he must also agree that 1 * 1/2 == 1/2, i.e. multiplication can indeed "make things smaller". Good luck, though. Crackpots aren't generally responsive to appeals to rational thinking.
I am replying to this post not because I disagree but because it postalogically fits the best (I am by no means an expert either).
IMHO, the crackpot in this regard is actually partially right, multiplication does mean that the number must get bigger, however for fractions you multiply four numbers, two numerators and two denominators. The resulting numerator and denominator by this multiplication get indeed bigger.
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