0^0

is widely accepted as 1.

proof being

a^0 = a^n.a^-n = \frac{a^n}{a^n} = 1

but with zero you get the paradox of

\frac{0^n}{0^n} = \frac{0}{0}

\frac{0}{n} = 0

and you can't divide by zero, so i dont see how you can use this proof to show 0^0 = 1

or am i missing something major.

Reply 1

nota bene

15

You're missing that it is widely accepted to be undefined - but in some contexts it makes sense to define it as 1, and therefore that is done.

edit: Or shall I rather say, that it can be defined differently depending on context, and sometimes is considered indeterminate (i.e. undefined).

Reply 2

Koudoo

You can divide by zero, its just if you have anything but zero on the top, you will have it equal to +/- infinity...

Reply 3

Totally Tom

18

Koudoo

You can divide by zero, its just if you have anything but zero on the top, you will have it equal to +/- infinity...

/thread.

Reply 4

Chaoslord

OP

16

so 0^0 = 1 is merely a conjecture... that makes a LOT more sense xD

Reply 5

username130457

2

In my AS-level text book it says: "Anything to the power of 0 is 1".

Hence, if we use the power of Language, 'anything' includes 0 in its formula.

Thus: 0^0=1.

Hope this helps. :smile:

Reply 6

Chaoslord

OP

16

Totally Tom

/thread.

i was thinking the same thing, hello my name is matthew and i declare you can divide by zero

fire away

Reply 7

Koudoo

Totally Tom

/thread.

Huh?

EDIT: Algebraically you can't, but theoretically you can...

Reply 8

Chaoslord

OP

16

Ramadulla

In my AS-level text book it says: "Anything to the power of 0 is 1".

Hence, if we use the power of Language, 'anything' includes 0 in its formula.

Thus: 0^0=1.

Hope this helps. :smile:

it also says that the rules of indices can be applied for a^n for any n that is rational

which is BS, n doesn't even have to be real xD

Reply 9

nota bene

15

http://en.wikipedia.org/wiki/0%5E0#Zero_to_the_zero_power

See that for more info (if you haven't already bothered to read it before posting here :p:

)

Reply 10

Chaoslord

OP

16

nota bene

http://en.wikipedia.org/wiki/0%5E0#Zero_to_the_zero_power

See that for more info (if you haven't already bothered to read it before posting here :p:

)

cheers im not a huge fan of wiki for maths info i find the minds on TSR more informative but the like "The choice whether to define 0^0 is based on convenience, not on correctness." sums it up in my eyes

Reply 11

Kolya

17

Chaoslord

it also says that the rules of indices can be applied for a^n for any n that is rational

which is BS, n doesn't even have to be real xD

What it says is true, and it is a common way of approaching some results. Remember that if

p \implies q

then

¬p \implies ¬q

is false.

Ramadulla

In my AS-level text book it says: "Anything to the power of 0 is 1".

Hence, if we use the power of Language, 'anything' includes 0 in its formula.

Thus: 0^0=1.

Hope this helps. :smile:

Type it into your calculator - see if that gives you one.

Reply 13

Chaoslord

OP

16

Mr M

Type it into your calculator - see if that gives you one.

haha thats what i did when i was trying to decide what it was a few weeks back xD

Reply 14

DescartesWasMyDad

8

Would it make more sense, generally, to not treat 0 on its own like an integer? You can't add it, divide by it, multiply by it, subtract it from anything, etc.

re. the 0^0 = 1 point. Isn't the n^0 = 1 point just a feature of the log function? I also seem to remember that you can't really do/use logs of 0s.

Reply 15

DeanK2

Ramadulla

In my AS-level text book it says: "Anything to the power of 0 is 1".

Hence, if we use the power of Language, 'anything' includes 0 in its formula.

Thus: 0^0=1.

Hope this helps. :smile:

You can't be serious?
Do you even think what you are posting. If this was the case, there would be no need for this thread.

idiot

DescartesWasMyDad

You can't add it, divide by it, multiply by it, subtract it from anything, etc.

k + 0 = k (Addition successful)

k - 0 = k (Subtraction successful)

k x 0 = 0 (Multiplication successful)

k / 0 = ? (Division unsuccessful)

3 out of 4 ain't bad.

Reply 17

DescartesWasMyDad

8

Mr M

k + 0 = k (Addition successful)

k - 0 = k (Subtraction successful)

k x 0 = 0 (Multiplication successful)

k / 0 = ? (Division unsuccessful)

3 out of 4 ain't bad.

It's a tautology though. It's like saying if I take this and do nothing to it, it's still itself. It's a completely pointless result and it doesn't behave like an integer.

DescartesWasMyDad

It's a tautology though. It's like saying if I take this and do nothing to it, it's still itself. It's a completely pointless result and it doesn't behave like an integer.

Ok let's abolish operations involving zero.

Oh heck, I can't solve this equation now!

(x + 1) (x - 3) = 0

Reply 19

DescartesWasMyDad

8

Mr M

Ok let's abolish operations involving zero.

Oh heck, I can't solve this equation now!

(x + 1) (x - 3) = 0

I'm not saying abolish it, I'm saying it should be treated differently. If we stopped trying to use it as an integer then we get rid of all the problems. It's a fairly new addition to mathematical symbolic logic. It isn't really a quantity, measure, etc.

0^0

Related discussions

Latest

Trending

Trending

Articles for you