taking a "power of 2" or "power of d" i was trying some of the problem in a few of the books i have and on more than one occassion cam across a question that referred to people in a game taking a "power of 2" or "power of d" or whatever. referring to taking counters or equivalent thing, such as moves on a board or whatever (so intergers only). now, what i was wondering is, naturally, one would assume in [tex]2^{n}[/tex] for a power of 2. n would be a natural number and equal to or bigger than 1. (whats the 'not equal to' sign in latex :S). however, after doing the problem assuming this, i suddenly wondered if [tex]2^{0} = 1[/tex] counted as a power of 2?? this is cause would cause complications in solving the problem but nothing too problematic. so, does [tex]2^{0} = 1[/tex] count? Im guessing it does, but just need to check. also, if the problem doesn't specifically revolve around integers, would an irrational power of 2 still count as a "power of 2"? such as [tex]2^{\frac{3}{2}}[/tex]. I'm guessing it still does, just need to check :D
1 is generally considered a power of 2, but it's sometimes excluded (just like 0 is sometimes excluded from the set of natural numbers). Just disregard it if it creates obvious troubles. Every positive number can be written as a power of 2 to a real number, so it would be meaningless to call [tex]2^{3/2}[/tex] a power of 2. Not equals is \neq in latex. :) [tex]1\neq 2[/tex]