Taking a power of 2 or power of d

[Trail_Builder]

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 occasion 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 $$2^{n}$$ 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 $$2^{0} = 1$$ counted as a power of 2??

this is cause would cause complications in solving the problem but nothing too problematic.

so, does $$2^{0} = 1$$ count? I am 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 $$2^{\frac{3}{2}}$$. I'm guessing it still does, just need to check :D

 

[Eighty]

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 $$2^{3/2}$$ a power of 2.

Not equals is \neq in latex. :) $$1\neq 2$$

 

[Trail_Builder]

thnx dude :D