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

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Homework Help Overview

The discussion revolves around the expression 1 raised to the power of infinity, questioning its value and meaning within mathematical contexts.

Discussion Character

  • Conceptual clarification, Assumption checking, Mixed

Approaches and Questions Raised

  • Participants explore the idea that 1 raised to any power equals 1, while others challenge the meaningfulness of treating infinity as a number. There are mentions of calculus and limits in relation to the expression, with some suggesting that the notation may imply a limit scenario.

Discussion Status

The discussion includes various perspectives on the expression, with some participants providing insights into the implications of treating infinity in this context. There is no explicit consensus, but several lines of reasoning are being explored regarding the nature of the expression.

Contextual Notes

Some participants note that the expression may be considered undefined or indeterminate, depending on the approach taken to infinity and the limits involved.

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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

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

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.
 

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