continued
All this to say, that qualitatively an infinite, non-terminating, possibly non-repeating number is no different than a finitely represented terminating number.
qualitative difference
Okay, I did say that quantitatively we can call an infinite set "one thing" but you were talking qualitatively, so I guess you could say that qualitatively an infinite set is different than one of its members. I would say it is still a single set. This is similar to the...
edit above:
in the above post, what I meant by top and bottom is, for each pair A-B, examine how many pairs have a 3 in either A or B (two-thirds of them), and for larger primes we'd have to consider how many have 3 and 5, etc. Then we also have to consider how many DON'T have higher primes...
One last question.
One last try, then I'll let it rest:
Does Anyone have Any ideas on how to prove all primes in a range are in Q? I'll take a suggestion of a half-baked possibility, anything may spark a creative solution. Probability and statistics (counting possible arrangements of...
Calling infinity "one thing" is not qualitative at all!
It's like: A pack of cards, A bussload of people, or a single proof (which contains many concepts that were themselves proven in proofs). A single set is an "object" which may be countably or even uncountably infinite if you examine the...
As was said, you can't disprove a definition. However, many useful branches of mathematics have been developed by CHOOSING different definitions. It's all about consistency. If you want to define something differently and then follow that definition to its logical implications, and if all of...
Thanks for the explanation of 1.
Any ideas on how to prove all primes in the range are in Q? I have worked for a long, long time (years) on it, but somehow the solution eludes me. I think I got "burned out" computing all primes < 1369, and now I have mathematical "writer's block" or...
Zero isn't allowed to be an exponent, though in one form "extra" primes can be added into the mix without losing anything from the proof except you won't be producing that particular prime in Q. But I'm more concerned with proving all primes in Q without these extra primes being put in A or B...
Matt,
Thank you for the confirmation of the theory. Request: could you point me in the right direction with a little more detail on how to prove ALL primes in the range are in Q? In particular, we know that we've eliminated all composites of the form ax-bx=(a-b)x but we've also eliminated...
summary?
I just realized I only read page 1.
So,
continuum => infinitely divisible => an infinite number of tasks and
discrete => A and B always are the same speed or stationary. This is, at least, what I think Canute was saying:
Quote: Canute said:
try working out the relative motion one...
closing a "hole" in the theory
Notice that in the example, not all primes less than 169 will be in Q. To get them all, it is necessary to divide the SAME SET of primes into piles A and B in different ways. We had 2 and 7 in pile A, the next step is to try 2 and 5 in A, or 2, 5, and 7 in A...
I've posted this theory elsewhere, so unless someone wants a real thorough exposition on it I won't go into all the details. If you've already read this elsewhere, I don't plan on addressing this here very long.
I've found a way to express prime numbers that seems (to me) to have the property...
A series is a special kind of sequence.
if your sequence is x1, x2, x3, x4, x5...
then the series it produces is x1, x1+x2, x1+x2+x3, x1+x2+x3+x4, ...
which we can re-label as y1, y2, y3, y4, ...
and this is a new sequence.
so if a progression is a series, then it is automatically...
draw picture with arrows
Don't try to think of the direction the ball is traveling over a long time, just think of the direction it is traveling for a tiny instant. That will give you the angle.