Recent content by acabus

1. Operations over infinite decimals numbers

0.999... does equal 1, see www.physicsforums.com/showthread.php?t=507001 [Broken]
2. Teaching myself calculus?

Calculus by Michael Spivak is really, really good if you want a thorough understanding of the concepts. The problems are all useful and challenging, and you learn a lot more than calculus in the process. However, I've heard it's quite hard compared to other calculus books, and you won't like it...
3. Absolute value

With absolute values, only the magnitude of the change matters. It doesn't matter if the change is positive or negative. So H must change more than TS.
4. Prove that a rational number squared has each of its prime factors with even exponent

So how does this work with \sqrt{18}, \sqrt[3]{7}, or \pi? I'm just trying to show that you may be overlooking some possibilities.
5. Alternative for sphere volume:FAIL

This is pretty much integral calculus, summing an infinite number of infinitely small areas. You should learn it, it's really useful.
6. Consecutive integers divisible by a set of Primes

I'll try to come up with a better one, mine's terrible. How on Earth did you work out frg(15)?
7. Consecutive integers divisible by a set of Primes

I calculated the first 8 and put them in to OEIS, and got: oeis.org/A072752. What you're after is not the gaps, but the difference, so it's one more than the terms in the sequence I linked to. I'm not sure about an efficient algorithm, my jumbled together program could only do 8 before taking...
8. Alternative for sphere volume:FAIL

So it seems to be (area of circle) * (circumference) * (1/2). It's less a question of why it doesn't work, than why your brother thought it would work. Maybe if you posted the derivation, we could point out the problem with it.
9. This bigger than grahams number?

Stop it. You're absolutely unimaginably nowhere near Graham's number, and it's pointless to try and come up with a larger number.
10. Possible values of X and Y for the problem

99 = 3 * 33, so 1 and 11 aren't the only values x or y can take. There's 1 solution to your problem. Don't be surprised that you're getting "ad hoc" methods, you've thrown together a few random arbitrary conditions, especially the "twin number" bit.
11. Possible values of X and Y for the problem

If x and y are whole numbers, then x/y can't be irrational.
12. Sum of Sums over Primes that Divide the Index

I think that's equivalent to \sum_{p=2}^{n} \frac{\left \lfloor n/p \right \rfloor}{p} , where the square brackets represent the floor function, and p runs through the primes less than or equal to n. I don't know if that helps at all, and no doubt it can be simplified more so.
13. Logic behind the number of combinations of numbers

It might help to imagine a tree diagram, with all the possibilities the numbers could be.
14. Has any equation ever been proved

Now I hate this kind of discussion, so I won't really get involved, but mathematics does not attempt to prove anything "in terms of the physical world", it has no concern for silly things like atoms and quantum systems.
15. Maths proof for fractions

My LaTeX always looks so ugly. n = \frac{(\frac{a}{b})}{(\frac{c}{d})} n\left(\frac{c}{d}\right) = \frac{a}{b} nc = \frac{ad}{b} n = \frac{ad}{bc} = \left(\frac{a}{b}\right) \times \left(\frac{d}{c}\right)