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## Homework Statement

Hi everyone,

I'm just wondering if someone could please clarify for me what infinity to the power of zero is? I seem to be finding conflicting opinions about this online. Is it '1' or 'not defined'?

Thanks!

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- Thread starter Pyroadept
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- #1

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Hi everyone,

I'm just wondering if someone could please clarify for me what infinity to the power of zero is? I seem to be finding conflicting opinions about this online. Is it '1' or 'not defined'?

Thanks!

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Thanks!

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HallsofIvy

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Mentallic

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It's undefined. Also we never say what infinite to the power of zero is, we instead express such results by the use of limits:## Homework Statement

Hi everyone,

I'm just wondering if someone could please clarify for me what infinity to the power of zero is? I seem to be finding conflicting opinions about this online. Is it '1' or 'not defined'?

Thanks!

## Homework Equations

## The Attempt at a Solution

[tex]\lim_{x\to \infty}x^{1/x}[/tex] is such an expression that would be of the form [itex]\infty ^0[/itex] and in this case it's equal to 1, but there are many other cases where it's not, such as [tex]\lim_{x\to \infty}\left(x^x\right)^{1/x}=\infty[/tex] or [tex]\lim_{x\to \infty} x^{1/\ln(x)}[/tex] which is a special one that equals the irrational number [itex]e\approx 2.718[/itex]

This is why expressions of this form are called indeterminate. They're undefined, until you find the specific question that defines them. It's different from the sense of 1/0 being undefined since that one is undefinable since it would create inconsistencies in our maths.

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