Subject: Re: Is 0 Nothing?
Date: Tue, 26 Sep 2000 23:14:28 -0400
From: Alex Bogomolny

Dina Zeliger wrote:

A power is the product of a number multiplied by itself a given number of times. i.e. n^k = n*n*...*n (k times). This definition in right when k>0. But, if k=0, how come the product of multiplying a number by itself zero times equals one?

The definition n^k = n*n*...*n (k times) only makes sense when k > 0, or even when k > 1!. k = 0 is a completely separate case and requires a separate definition.

zero is basically nothing.

Zero is not nothing. There's a difference between 1 followed by nothing which is just 1 and 1 followed by 0 which is 10.

its value is not a quantity,

and what is "quantity"?

i.e. zero times something is nothing - zero.

Which proves nothing but is not zero!

in that case, how is it possible that n^0=1.

By definition.

multiplying n by itself zero times equals nothing, since you don't multiply it at all.

That's right. The reason for that definition is different.

That theory also suggests that 0^0=0,

Do not see what theory you are talking about.

and that this expression is not indefinite.

Every definition must have some reasons. 0^k = 0 is only meaningful because n^k = n*n*...*n (k times). So that k > 1. You can't derive from here 0^0 = 0!

if (n^0=0) and (0^n=0) then (0^0=0).

Nonsense. Both only make sense when n is not zero. You can't quote any thing rule you might have studied that allows for that implication. The form

if blah-blah and blah-blah then blah-blah

is not necessarily a correct derivation.

Regards,
Alexander Bogomolny