Question

Why is 0! = 1 by definition; but 0^0 is an indeterminate form?

Answer 1

! <------Because of this...maybe

Answer 2

im curious because x^0 is bad form since it can result in 0^0; but why not define it as 1 with the rest of normailty :)

Answer 3

even I am curious about that

Answer 4

don't change it to 1 ! it will mess up a lot of math ppl already did in the past. just keep the status quo!

Answer 5

but imran told me 1^0 is 1 ...2^0 is 1 and 2^1 is 2 so 0^0 is indeterminate

Answer 6

yep; 0^0 is a bad an apple as 1/0 ....

Answer 7

but if you get 0!, well, thats just fine lol

Answer 8

lol

Answer 9

Actually, 0! = 1 by contemporary tradition. Many people claim that it is 0 via proof. A lot of well known math and applied physics professors have claimed that 0! = 0 and keep 0! = 1 simply because our formulas break down without it true.

Answer 10

well, amistre - you know, google is taking over the world.
and they are thinking the same as you !!!

http://www.google.com/#hl=en&cp=3&gs_id=b&xhr=t&q=0^0&qe=MF4w&qesig=P_7nEjebZ63RBy_0L3TWtA&pkc=AFgZ2tmznUgQ768b34VKG_p3k9L1-owtjcHfUX4llZ-f1m6qKvPdDvoBqjCKZLPpL2vTTLs2LErF4wXiMlC_5NNUjW1fA8pjuA&pf=p&sclient=psy&site=&source=hp&pbx=1&oq=0^0&aq=0&aqi=h1g5&aql=&gs_sm=&gs_upl=&bav=on.2,or.r_gc.r_pw.r_cp.&fp=7f38cb74ed69968b&biw=1440&bih=700

Answer 11

Theres an awesome site that has professor proofs of 0! = 0 let me see if i can find it

Answer 12

lol ... google 0^0 = 1, i love it

Answer 13

Lol

Answer 14

and we had doubts today about wolfram Ishaan :)

Answer 15

what did wolfram do?

Answer 16

he was smart ! that tells us what we were.

Answer 17

Indeterminate
http://www.wolframalpha.com/input/?i=0^0

Answer 18

Lol

Answer 19

i seen that as well

Answer 20

it began me thinking with why we have 2 rules for derivatives;

d\dx (x) = 1

d/dx (x^n) = n*x^(n-1)

Answer 21

d/dx (x^1) = 1*x^1-1 = 1*x^0 ..right?

Answer 22

but this goes bad when x=0 .... for some reason that cant be defined

Answer 23

Right

Answer 24

http://www.adonald.btinternet.co.uk/Factor/Zero.html

Answer 25

interesting i guess

Answer 26

its a cute story :)

Answer 27

but check this out :)

http://www.wolframalpha.com/input/?i=y+%3D+x^0+at+x%3D0

Answer 28

That is so confusing

Answer 29

That's why it's called indeterminant - nobody know what the heck to do with it.

Answer 30

Lol

Answer 31

But seriously I am very confused now...

Answer 32

hold on. there is lots of controversy (ok a little) still about what
\[0^0\] is
of course as a statement about limits it is indeterminate, but as a symbol many define it to be 1. those are different issues

Answer 33

wolfram seems to be schismed about it as well

Answer 34

0^0= bad form

http://www.wolframalpha.com/input/?i=0^0

but, f(x)=x^0 ; f(0)=1

http://www.wolframalpha.com/input/?i=y+%3D+x^0+at+x%3D0

Answer 35

some sources here
http://mathforum.org/dr.math/faq/faq.0.to.0.power.html

Answer 36

we seem to be in my own little universe ... all i see is my questions, and i cry ...

Answer 37

There once was a student from Trinity,
Tried to take the square root of infinity.
Whilst counting the digits
Was seized with the fidgets.
Gave up math and took up divinity.

Answer 38

only one of two clean ones i know

Answer 39

limericks eh ... that was a good read.

Answer 40

i like the 0^x is rather unimportant; yet if 0^x = 0 for the most part; then why would we attribute it to 0^0 = 1 instead of 0

if x^0 is 1 for the most part, how can we define it as 0 as well.

and of course they have different limits and such

Answer 41

not particularly one of the best but one of the few i would post here