0 / 0 = ?

The fallacy is the implicit assumption that dividing by 0 is a legitimate operation with 0 / 0 = 1

0x1 = 0
0x2 = 0
so
0x1 = 0x2
and by division with 0
0/0 + 1 = 0/0 +2
so we have
1=2
or
0/0 - 0/0 =2 -1
and
0 = 1
It is generally regarded among mathematicians that a natural way to interpret division by zero is to first define division in terms of other arithmetic operations. Under the standard rules for arithmetic on integers, rational numbers, real numbers and complex numbers, division by zero is undefined. Division by zero must be left undefined in any mathematical system that obeys the axioms of a field

 

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yes but if some say 0/0 = 0
then
0x1 = 0x2
so i put
0/0 =0 there
and
i have
0/0 x1 =0/0 x 2
0x1/0=0x2/0
0x0 x 0x2 = 0x0 x 0x1
so we have
0(0+2) =0(0+1)
that will mean
0(0+2)/0(0+1)=1
and there is
0+2/0+1 =1
so
0+2=0+1
0=2-1
0=1

 

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Ok. Aparently the original question is answered.

 

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If 0/0 can be any number then it can be a prime, in which case other numbers are ruled out and vice versa.


As to the equation, it's a nice party trick, that's all

 

0/0 can be any number you choose, simple as.

Although it is not wise to use such calculations.

 

Ok, I choose 42.

 

You're free to have this as an axiom, if you choose. However, if you study groups and rings (rings are groups with an added operation) then you will see that rings with 1 = 0 aren't very interesting.

The moral of the story? We choose axioms that generate the most interesting mathematics.

 

0 cannot be added to, divided into, subtracted from or multiplied.

 

umm your half right and half WRONG.

0 CAN be added to, if i have no oranges and i buy an orange i now have 1 orange.

0 CAN be subtracted IN CERTAIN CURUMSTANCES, the most ovious being money. If you have no money you can borow money which will mean you have to pay it back and your balance sheet will be in the red rather than the black

0 CAN be multiplied, it just equals zero

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its only when you get to dividing zero an issue comes up, even then its only when you divide BY 0 not when you DIVIDE zero.

0/1= 0
1/0= undefined

 

No oranges doesn't exist. You can't add to something that doesn't exist.
If that makes accounting easier, fine. But it's pretending for the sake of convenience.
No. Nothing cannot be multiplied.

 

Do mathematicians actually agree with this, or is Yorda being humorous.
Pardon me, my maths is not good enough to see the joke.

Take the example of a suit, mentioned earlier.

In a room there is a wardrobe.
In that wardrobe there are socks, cardigans, and shirts, but no suits.

In the room itself are a group of people.
There are Indians, Thais, and Russians, but no Germans.

Are we saying that in the wardrobe there are any number of suits for Germans?

No. There are just no suits.

0/0=0

 

I've always wondered, multiplication seems just like a convenient way to do addition, is there any situation where this isn't true?

 

Bull! If there are no Germans, there are no ways to divide the suits among Germans.

 

0/0 equals 0*(0/0) equals 0.