Why is zero to the zero power not equal to one?
2006-08-19 20:04:19 · 19 answers · asked by Jerry M 3 in Science & Mathematics ➔ Mathematics
0^0 is not equal to one since 0^0 can be expanded to:
(0^x)/(0^x) because applying the laws on exponents, this simplifies to 0^(x-x) or 0^0. Since in (0^x)/(0^x), 0^x is equal to 0, such that x is equal to a non-zero real number, when this is simplified using the realized fact, it becomes 0/0 and so, now, this cannot equal to 1 becuse this is an indeterminate number. This is why 0^0 is not equal to 1.
(It's not 0 either.)
2006-08-19 20:51:51 · answer #1 · answered by fictitiousness ;-) 2 · 0⤊ 3⤋
L has got it right. In math it is sometimes convenient to *define* things in such a way that may seem confusing but makes things work out nicely. This is one of those times. If we ignore the case x=0, then x^0=1 and 0^x=0. If we try to define a value for 0^0 then only one of these formulas can win out. In mathematics things of the form x^0 occur more often than things of the from 0^x so it is widely accepted that the x^0=1 formula should be extended to include the case when x=0 instead of the 0^x formula.
2006-08-20 04:01:12 · answer #2 · answered by TA Timmy 2 · 0⤊ 0⤋
zero is a special case in alot of problem. It seems weird that any other number to the zero power is 1 but think of it this way zero to any power is zero, so why should 1 be any different? Zero is just undefined in this case though.
2006-08-20 03:14:15 · answer #3 · answered by Abtsolutely 3 · 0⤊ 0⤋
Thats the wrong way around, 0^0=1
http://mathforum.org/dr.math/faq/faq.0.to.0.power.html
Its controversial, 0 times anything is zero, while anything to the zero power is 1. Basic math says that 0^0 must be 1 because the equation approaches a limit, which makes me wonder why Calculus defines it as a indeterminate form.
2006-08-20 03:16:29 · answer #4 · answered by ∟ 1 · 3⤊ 0⤋
because zero to the power of one is also zero than how can zero to the power of zero be one
so zero to the power of zero is not equal to one
2006-08-20 03:11:51 · answer #5 · answered by Vatsal S 2 · 0⤊ 0⤋
Because in mathematics, division by zero is not defined.
0^0 has division by zero
0^0 = 0^(1-1) = 0^1 x 0^-1 = 0/0 (not defined)
2006-08-20 04:54:59 · answer #6 · answered by ideaquest 7 · 0⤊ 1⤋
Because all products of 0 are 0.
2006-08-20 03:10:36 · answer #7 · answered by halosfan2003 2 · 0⤊ 0⤋
i love math.
0 to the 0 power = 0
it doesnt = 1 because you cant take 2 nothings and make it something.
2006-08-20 05:19:35 · answer #8 · answered by shy 2 · 0⤊ 0⤋
Graph y = x^x (if x is zero, you get 0^0)
As x approaches zero, y approaches 1
http://www.coolmath.com/graphit/
2006-08-20 17:12:03 · answer #9 · answered by Anonymous · 0⤊ 0⤋
because 0^0 meanszero multiplied by 0 to zero factors
doesn't it sound wierd.so it is indeterminate and not 1
2006-08-20 03:11:39 · answer #10 · answered by raj 7 · 0⤊ 0⤋