Recent content by acabus

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    Operations over infinite decimals numbers

    0.999... does equal 1, see [Broken]
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    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...
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    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.
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    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.
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    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.
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    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)?
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    Consecutive integers divisible by a set of Primes

    I calculated the first 8 and put them in to OEIS, and got: 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...
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    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.
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    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.
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    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.
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    Possible values of X and Y for the problem

    If x and y are whole numbers, then x/y can't be irrational.
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    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.
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    Logic behind the number of combinations of numbers

    It might help to imagine a tree diagram, with all the possibilities the numbers could be.
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    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.
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    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)