0 power to 0 = 0 or 1? :)

@eranushka-4BgWe8 • Oct 27, 2024

Oct 27, 2024

1.1K

Hi again 😀 Sorry for asking too many questions, but I "have to" clear my mind 😀

As we know for other numbers we get "1" but what about 0, 0 power to 0? 😀

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jaspal rautela

@jaspal-rautela-yw5rJz • Sep 25, 2012

undefined.......
ErAnushka

@eranushka-4BgWe8 • Sep 25, 2012

jaspal rautela
undefined.......
are you sure? 😕
jaspal rautela

@jaspal-rautela-yw5rJz • Sep 25, 2012

yes...
ErAnushka

@eranushka-4BgWe8 • Sep 25, 2012

jaspal rautela
yes...
Okay 😀 Thanks 😀
Kaustubh Katdare

@thebigk • Sep 25, 2012

Check this page - <a href="https://www.askamathematician.com/2010/12/q-what-does-00-zero-raised-to-the-zeroth-power-equal-why-do-mathematicians-and-high-school-teachers-disagree/" target="_blank" rel="noopener noreferrer">Q: What does 0^0 (zero raised to the zeroth power) equal? Why do mathematicians and high school teachers disagree? | Ask a Mathematician / Ask a Physicist</a>
ErAnushka

@eranushka-4BgWe8 • Sep 25, 2012

The_Big_K
Check this page - <a href="https://www.askamathematician.com/2010/12/q-what-does-00-zero-raised-to-the-zeroth-power-equal-why-do-mathematicians-and-high-school-teachers-disagree/" target="_blank" rel="nofollow noopener noreferrer">Q: What does 0^0 (zero raised to the zeroth power) equal? Why do mathematicians and high school teachers disagree? | Ask a Mathematician / Ask a Physicist</a>
Okay 😀
vinod1993

@vinod1993-r3yTlk • Sep 26, 2012

Obviously 0^0 is one. How?
Let us assume x=0^0.
So take logarithm on both sides,
ln x= ln (0^0)
Using logarithmic rules,
ln x = 0*ln(0)
So here we arrive at a conclusion, zero multiplied by infinity(indeterminate to be precise). It's zero, for those of you who argue on this let me try telling this how,
0*ln0 can be written as lim(x->0+) sin(x)*lnx. Because at x=0, sinx=0
sin(x)*lnx = lnx/cosec(x). So, if we apply l'hopital's rule twice we arrive at,
lim(x->0+) {[cos(x).tan(x)]+[sin(x).sec^2(x)]} which is equal to zero.
so that implies, ln x=0 => x=e^0=1.
Therefore, 0^0 is one.! 😀
Abhishek Rawal

@abhishek-fg9tRh • Sep 26, 2012

Nice debatable question Anushka,
0^0 can have two approaches.
Read this :
<a href="https://www.askamathematician.com/2010/12/q-what-does-00-zero-raised-to-the-zeroth-power-equal-why-do-mathematicians-and-high-school-teachers-disagree/" target="_blank" rel="nofollow noopener noreferrer">Q: What does 0^0 (zero raised to the zeroth power) equal? Why do mathematicians and high school teachers disagree? | Ask a Mathematician / Ask a Physicist</a>
#-Link-Snipped-#
ErAnushka

@eranushka-4BgWe8 • Sep 26, 2012

#-Link-Snipped-# True, thanks 😀

#-Link-Snipped-# Yes, I read that already, as #-Link-Snipped-# said 😀

Thank you guys 😀
zaveri

@zaveri-5TD6Sk • Oct 19, 2012

any operation performed on zero alone yields zero
vinod1993

@vinod1993-r3yTlk • Oct 20, 2012

zaveri
any operation performed on zero alone yields zero
Not applicable to all operations #-Link-Snipped-# since 0!=1. 😀
manishks

@manishks-AZybhs • Oct 22, 2012

0^0 is an indeterminate form. Its undefined. Its neither 0 nor 1.
indeterminate forms include 0^0, 0/0, 1/∞, ∞ − ∞, ∞/∞, 0 × ∞, and ∞^0
😀
vikaskumar11233

@vikaskumar11233-J10JeV • Dec 10, 2012

0 to the power 0 neither gives you 0 nor 1 as a result. It is undefined.