Should 00 be 0 or 1?
This has always been a strong frustration source for me.
if you ask the calculator, it says it is zero.
however, the alternating sum of binomial coefficients from the n-th row of Pascal's triangle is what you obtain by expanding (1-1)^n using the binomial theorem, i.e., 0n.
But the alternating sum of the entries of every row except the top row is 0, since 0^k=0 for all k greater than 1.
But the top row of Pascal's triangle contains a single 1, so its alternating sum is 1, which supports the notion that (1-1)^0=0^0 if it were defined, should be 1.
so therefore 0^0 is zero.
i hope this helped,
00 is an indeterminant form...here's why ...
Note...if we let n be any real number...we have
00 = 0 n-n = 0n / 0n = 0 / 0
But also note that 0 / 0 = pi or 0 / 0 = 11 or 0 / 0 = e ...... etc....
Thus....we can't actually determine the value of 0n-n = 00