What is the value of infinity to the power zero?

Question

This is a mathematical question.

Answer 1

Depends on hopw do you define the infinity.
If you extend the Real numbers set, you may say that infinity is defined as the NUMBER, which is bigger than any of the numbers in the non-extended Real numbers set. In that case infinity to the power of zero is 1 because any Real NUMBER to the power zero is 1.
But when you calculate limits, infinity to the power zero is indeterminate.
For example:
lim(x^(1/x)) when x-->infinity.
There x is considered as infinity, while 1/x is considered as zero. So we have infinity to the power of zero, but we cannot say that the limit equals 1. To calculate the limit we gotta do some manipulations before we say the result.
In our case
lim{x^(1/x)} = lim{e^ln[x^(1/x)]} = lim{e^[(lnx)/x]} = lim{e^[(x-1)/x]}=
lim{e^[1-1/x]}=e
As you see, this limit doesn't equal 1.

Answer 2

1

Answer 3

For any non-zero x, x^0 is 1.

Therefore, infinity to the power of zero is also 1

Answer 4

it is 1

Answer 5

Infinity is more a concept than a number, as no value can ever be placed upon it. Therefore, infinity raised to the zero power is undefined.

Answer 6

Infinity to the zeroth power is indeterminate, just like zero divided by zero is indeterminate.

There are seven indeterminate forms, of which 0/0 is just the best known. They are:
- zero divided by zero
- infinity divided by infinity
- zero times infinity
- infinity minus infinity
- zero to the zero power
- infinity to the zero power
- one to the infinite power

You can fiddle around with any of these forms to get them to be any value you like. That's why they're called "indeterminate".

Answer 7

x to the zero power = 1
infinity to the zero power = 1

Answer 8

Anything to the power zero is One (1).

Answer 9

1. Anything to the power of 0 is 1.

Answer 10

only 1