# What does 0^0 equal?
**URL:** https://boards.straightdope.com/t/what-does-0-0-equal/183676
**Category:** Factual Questions
**Created:** [June 23, 2003, 2:34am UTC](https://boards.straightdope.com/t/what-does-0-0-equal/183676 "2003-06-23T02:34:39Z")
**Posts on this page:** 5
**Page:** 1
### Author:  [@quelquechose](https://boards.straightdope.com/u/quelquechose)
#### Post date: [June 23, 2003, 2:34am UTC](https://boards.straightdope.com/t/what-does-0-0-equal/183676/1 "2003-06-23T02:34:39Z")
I was always taught that 0^0 was equal to 1. Most textbooks I have seen say that it equals 1, and my TI-89 agrees. However, one of my textbooks says it is undefined, and a Google search shows that some other people say so as well. So what is it: 1, undefined, or something else? Is my textbook wrong or is my calculator?
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### Author:  [@kunoichi](https://boards.straightdope.com/u/kunoichi)
#### Post date: [June 23, 2003, 2:44am UTC](https://boards.straightdope.com/t/what-does-0-0-equal/183676/2 "2003-06-23T02:44:44Z")
I thought it equalled one, but it makes sense if it’s undefined. I’d go with the textbook or a math teacher/professor for the honest truth, though. As for the TI-89 saying it equals one, well… the unfortunate side-effect of such wonderful machines is that people think they’re right all the time. The trick is knowing when they’re wrong. I had a TI-85, and I remember it giving me an answer for an expression that shouldn’t have one (I think it was inverse sine or something that only works between -1 and 1, but I can’t remember ;)).
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### Author:  [@scr4](https://boards.straightdope.com/u/scr4)
#### Post date: [June 23, 2003, 2:50am UTC](https://boards.straightdope.com/t/what-does-0-0-equal/183676/3 "2003-06-23T02:50:27Z")
The limit of X^0 as X-\>0 is 1. (2^0=1, x^0=1, so 0^0=1)
The limit of 0^X as X-\>0 is 0. (0^2=0, 0^1=0, so 0^0=0)
So it’s undefined. Or you need to choose one depending on the circumstances.
By the way my HP-32sII calculator says “Invalid.”
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### Author:  [@kunoichi](https://boards.straightdope.com/u/kunoichi)
#### Post date: [June 23, 2003, 2:53am UTC](https://boards.straightdope.com/t/what-does-0-0-equal/183676/4 "2003-06-23T02:53:50Z")
[http://mathforum.org/library/drmath/view/55764.html](http://mathforum.org/library/drmath/view/55764.html)
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### Author:  [@raygirvan](https://boards.straightdope.com/u/raygirvan)
#### Post date: [June 23, 2003, 3:26am UTC](https://boards.straightdope.com/t/what-does-0-0-equal/183676/5 "2003-06-23T03:26:10Z")
See the [sci.math FAQ for 0^0](http://www.faqs.org/faqs/sci-math-faq/specialnumbers/0to0/). The result has been argued-about and depends on mathematical context … but the FAQ concludes that most mathematicians view 0^0=1 as the most useful convention to adopt, as it stops 0^0 being a special case in many circumstances (for instance, the binomial theorem).