Friday

December 19, 2014

December 19, 2014

Posted by **sammy** on Tuesday, January 22, 2008 at 8:03pm.

- math (extra credit)! -
**Count Iblis**, Tuesday, January 22, 2008 at 8:27pmConsider first positive powers. Let's define:

f(a,n) = a^n

where a is a real number and n is a positive integer. This is well defined:

f(a,n) = a^n =

a*a*a...(n-factors in total).

Now, we haven't defined f(a,n) when n is not a positive integer, so, in theory, you are free to extend the function f(a,n) in any arbitrary way to other numbers. However, the function

f(a,n) has some nice properties and you want to preserve those when you extend the definition of f(a,n).

E.g.:

f(a,n+m) = f(a,n)*f(a,m)

If we want to extend the function to

n = 0 while not violating this equation, then we must choose f(a,0)= 1. To see this, take m = 0, in the above equation:

f(a,n) = f(a,n)*f(a,0) --->

f(a,0) = 1.

So, what mathematicians have done here (and in many other cases) is to take some of the properties of the function they want to extend to a larger set as the definition of the function (they uniquely define the function).

- math (extra credit)! -
**sammy**, Tuesday, January 22, 2008 at 8:46pmthx but this didnt help i need to know why n^0= 1

- math (extra credit)! -
- math (extra credit)! -
**Damon**, Tuesday, January 22, 2008 at 8:52pmHe told you, and I think it was the coolest answer yet!

**Answer this Question**

**Related Questions**

dividing monomials - i dont know what to do when their is a smaller number on ...

Math - Exponential Notion - Can someone explain this to me please, I cannot help...

algebra - It's a monomial and we are told to simplify and assume no denominator ...

math - domain of f: any real number domain of g: any real number except x is not...

math derivative please help - the derivative of 2x^e is zero right or no? do i ...

math-please help - Explain why the slope of a horizontal line is zero, and the ...

math... help plz (not hard) - Why is it that everything to the ZERO power equals...

Math - Wha are the roots of x to the second power divided by x minus six equals ...

math trivia! - Take any number ending in 5. (for example 35). Multpily the first...

algebra - 7s over 5t to the negative 3rd power 2 to the negative 3rd power times...