the cases when two irrational numbers have an irrational product
.
I'm probably being totally naive, but I'd have thought it is not too hard to show that two irrational numbers (a, b) have an irrational product if a and b are not equal, and a is not the reciprocal of b.
Not...
decimal fractions, time etc
Slight digression, but no-one here has been following the effect of decimalisation of price quoting on American stock exchanges the last couple of years by any chance?
My hunch at the time, and the industry consensus now, was that the increased number of quotable...
texts on number theory
Maybe start with online articles on number theory rather than books?
Most textbooks on number theory are a bit unsatisfactory, since most of the classic problems that have been solved were solved by creating or importing chunks of new maths [abstract algebra, galois...
numbers, fractions, time
Seems to me that the idea of a start to time is quite paradoxical enough on its own without having to worry about how the first instant or time unit "gets started".
I suppose those loopy-string people are hoping the idea of a start to time is just going to drop out...
teleporters and stuff
.
Looks like I'm not just a coward but in the minority.
I regret to admit I would be very suspicious of any machine claiming to make copies of me or otherwise generate a situation where I might die and others might or might not notice.
Sad eh?
.
conditions for odd perfects if any exist
.
Loop quantum & kebz33, the condition that sounds most interesting to me is that one about any odd perfect having to be, should there be any, a product of a square number and a prime number raised to an odd power.
If I remembered that right.
.
odd number of proper factors in a square
.
Perhaps I misunderstand, but isn't it enough to show that an odd perfect number cannot be square, to note that in most numbers the proper factors can be paired as a, total/a; b, total/b; c, total/c etc, and that in a square there is one pair [sqroot...