Shouldn't 0*0=undefined?

Question

Okay, please correct me if I am an idiot, but as of now, 0*0=0. Think about 0*0...it's saying that you have NO zeros...if you have no zeros, how do you end up having 0? If you have no nothing, you have something...but it could end up being any possible number EXCEPT 0, putting it at undefined pretty much.

Also...2*3=6, 6/3=2. 0*0=0, 0/0=undefined.

I believe that with the 0 equations, they should both be equal, but they aren't because 0*0=0 =/.

Please enlighten me :). Thanks.

Answer 1

There are certain axioms from which all of our rules about numbers are derived. One of these axioms says that real numbers are closed under multiplication. This means that if you multiply ANY two real numbers together you get another real number.

So since 0 is a real number 0*0 is also a real number. Thus is can not be undefined. Showing that 0*0=0 is a bit harder, but I'll try.

Since 0 = 1 + (-1) we can say that [1 + (-1)]*0 = [0]*0. Distributing the zero through the brackets on the left hand side give us

(1)0 + (-1)0 = 0*0

Since (1)0 = 0 and (-1)0 = 0 we have

0 + 0 = 0*0

And 0 + 0 = 0 so

0 = 0*0

Answer 2

0 * 0 = 0² So now, what does 0² equal to, I would say it's zero.

If you have nothing, then you have nothing. Nothing is not Something.

2/2 = 1
1/1 = 1
0/0 = ? I believe it should be 1 even if the Mathematical world agrees or disagrees.

1/0 = ∞ If you can't get to infinity, how do you know for sure if the answer will be infinity?

10/2 = 5
9/2 = 4∙5
↓ ↓ ↓
1/2 = ½ We can see the answer getting smaller all the time.
0/2 = 0

0/ x = 0
0/ 0 = 1 ?????
x/ 0 = ? Undefined.

Answer 3

anything * 0 = 0. Proof:

x * 0 = x * (0 + 0) --->
x*0 = x*0 + x*0 ---->
-(x*0) + x*0 = -(x*0) + x*0 + x*0 --->
0 = 0 + x*0 --->
0 = x*0.

And here's something fro Brenmore (below me). You argue that 0/0=1 because 2/2=1, 1/1=1, so 0/0 should be 1 as well. But the reason 0/0 is undefined is because this argument can be made for any number. I can "prove" to you that 0/0=100 using the same kind of logic:
500/5 = 100
400/4 = 100
300/3 = 100
200/2 = 100
100/1 = 100
Therefore 000/0 = 0/0 = 100 as well!

Answer 4

I think you're making a confusion between "not", and "nothing".

0 * 0 means nothing, multiplying nothing times. Which is still nothing. It is quite different from "no nothing". Quite.


as for the 0*0=0, but 0/0 is undefined, argument, I'm afraid it also fails. Why? Because, by definition of the division, it is NOT valid if the diviser is 0.


Hope this helps

Answer 5

Aryabhata's Rule
x + 0 = x
x - 0 = x
x * 0 = 0
0/x = 0

Additional Arabic Rule
x/0 = infinite
0/0 = indeterminate
x^0 = 1

These are the basic ground rules of mathematics. Except, x^0 = 1, no other can be proved. These are the basis on which mathematics has been derived. You may yourself start with a new basis and start a new mathematics. But these are and the will remain the widely accepted basis for mathematics.

Answer 6

for me... it is still 0(zero)
in the equation: 0*0=0 factors 0 has a still a value of 0, therefore 0 is 0.

undefined is use when the denominator is 0

ex: 4/0 = undefined.

Answer 7

0 = 0/1
the bottom part is 1 so it is defined, just like:
0*0 = (0/1)*(0/1) = 0/1 = 0
while 0/0 which bottom part is 0, in a fraction, the bottom part cannot be 0 or it is undefined:
that is why 0/0 is undefined but 0*0 is not :)

Answer 8

To have nothing and multiply it by nothing leaves you with nothing. However to have 1/0 means you are dividing 1 into zero parts....which makes no sense, thus it is undefined.

Answer 9

Yes.when u say that 0*0= undifined that is right....0*0=Infinite...i will show u how.

we know that...1*0 = 0...now if we multiply both sides by 0 then it will be like this...1*0*0 = 0*0
therefore if we tranfer LHS 0*0 in denomonator then,

1 =0*0/0*0 ....so now if at all 0*0 = 0 then ans will be 1 = 0/0...which is not correct....

This will apply to 2 ..3...4....5....100.......infinite nos...

So, 0*0 = Infinite

Answer 10

0 is a methematical number. And it does not matter how much you multiply it, you still end up with zero. Example 5 times nothing is nothing.