Recent content by TauCrouton

True, I see your point. Although if we don't limit ourselves to the definition of real numbers, I suppose there is a theoretical number which does come infinitely close to one. Like if you type 0.999999999... you can hold the 9 button for as long as you like, but it will never truly reach 1...

first, rewrite the square root as an exponent, and rewrite 1 as log(10), so you get 0.5log(2x-1) + log(x-9)^(1/2) = log(10) Bring the exponent down to get 0.5log(x-9) 0.5log(2x-1) + 0.5log(x-9) = log(10) multiply both sides by 2 log(2x-1) + log(x-9) = 2log(10) Raise the 10 in the log...

I'm not saying its not, I'm saying 0.999999999... isn't technically 1, just infinitesimally close to 1. (see below) I meant to say the 0.99999... is a repeating 9 not a discreet value of "0.999999999", if that clears things up. Either way, it is an interesting technicality. The way I...

0.9999999999 technically can't be 9/9, although that is the answer. Interesting things, infinite sums.

I think you can just use 0.54 as you first term and use a common ratio of 0.01.Edit: Yes, it works. I haven't gone through the other methods posted here, but there is definitely more than one way to go about it. The way I posted is the one that makes the most sense to me, so just find one that...

You can use the sum of an infinite geometric sequence formula. S = \frac{a}{1-r} your a value is (in this case) 0.7. You want to make a series that will create 0.77777777777... etc. To make this series, 0.7 is your first term. It is multiplied by the common ration (r) 0.1 to get 0.07 (your...

Although String Theory says otherwise ;)

One thing to keep in mind is that the water will bend and refract the light. Good ol' Snell's Law.

I've got myself a pretty dandy collection of physics and maths books. Cosmology/Astrophysics Foundations of Modern Cosmology by Hawley and Holcomb The Science of the Universe by Harrison Relativity and Cosmology by Kaufman III Inner Space;Outer Space: The Interface Between Particle Physics...