Yes, you are correct. The answer to 1^infinity is 1.

[Success]

Homework Statement

What's 1^infinity?

Homework Equations

I think the answer is 1 because 1 to the power of anything equals 1, am I right? What's the answer to this?

The Attempt at a Solution

 

[phinds]

Yes, you are right, although I don't think it's a particularly meaningful question because it treats infinity as a number which is often not really appropriate.

 

[physics604]

You can prove it equals 1 through calculus, but it is actually undefined because infinity isn't a real number.

 

[Dick]

Homework Statement

What's 1^infinity?

Homework Equations

I think the answer is 1 because 1 to the power of anything equals 1, am I right? What's the answer to this?

The Attempt at a Solution

That notation is usually shorthand for a limit a^b where a approaches 1 and b approaches infinity. If a is exactly 1, then yes, the limit is 1. Otherwise it's indeterminant (it could be anything) and the limit depends on the exact behavior of a and b.