Probably a simple question and possibly not asked very well. What I want to know is..
In binary, a decimal value of 1 is also 1.
It can be expressed as $x = 1 \times 2^0$
Question:
Why is two to the power of zero equal to one?
I get that two to the power of one is equal to two, or binary 10, but why is to the power of zero equal to one, is this a math convention? is there a link I could read?
Best Answer
Because we want $2^{m+n} = 2^m \cdot 2^n$, and if $n = 0$ this requires that $2^0 = 1$. More combinatorially, $a^b$ is the number of functions from a set with $b$ elements to a set with $a$ elements, and there is exactly one function from the empty set to any other set (the empty function). This is the same reason that $0! = 1$.