Why 0^0 = 1?

[e3c6]

0^0 is defined in Julia, and equals 1. Mathematically 0^0 is undefined.I think other programming languages leave it undefined, although Python sets 0^0 = 0 (which is insane in my opinion).

To me it makes sense to make 0^0 = 1 (it turns out to be useful in some code I am writing right now, preventing some ifs and making things easier).

But I was wondering what other people think about this. Why was this approach selected in Julia?

[giordano]

@e3c6

0^0 is defined in Julia, and equals 1. Mathematically 0^0 is undefined.

Yes but there are some reasons to take 1 as value:

• https://www.math.hmc.edu/funfacts/ffiles/10005.3-5.shtml
• algebra precalculus - Zero to the zero power – is $0^0=1$? - Mathematics Stack Exchange
• http://www.askamathematician.com/2010/12/q-what-does-00-zero-raised-to-the-zeroth-power-equal-why-do-mathematicians-and-high-school-teachers-disagree/

@e3c6

I think other programming languages leave it undefined, although Python sets 0^0 = 0 (which is insane in my opinion).

No, in Python 0 raised to power 0 is 1:

>>> 0**0
1

@e3c6

Why was this approach selected in Julia?

Look to the code in base/intfuncs.jl. Basically, if the exponent is 0 the returned value is always 1.

[pabloferz]

Just as an additional curious note, here’s a nice reference where Knuth argues why 0^0 should be 1:

9205211.pdf