What does 1/0 equal? What does 0/1 equal? What does 0/0 equal?

Question

How can I write a proof?

Answer 1

any number divided by zero is undefined, since zero goes into any number an indefinite/infinite # of times.

zero divided by any number besides zero = zero. zero halves, zero thirds, zero tenths, etc all = zero.

Answer 2

0/1 is easy - its zero.
Anything divided by 0 is infinity except for 0/0 which is indeterminate.

How do you prove it - ahh sorry cant do that, but I can show why you cant determine what 0/0 is. With the schoolboy proof that 1=2


Basic algebra
1, A = B
Multipy both sides by A
2, A*A = B*A
Substract B*B from both sides (B squared)
3, A*A - B*B = B*A - B*B
now expand out
4, (A+B) (A-B) = B(A-B)
now divide both sides by (A-B)
5, (A+B)((A-B)/(A-B) = B(A-B)/(A-B)
6, (A+B) = B

Now Let A=1
7) 1+B=B
But at the beginning 1) A=B
Therefore
8) 1+1= 1
So
9) 2 =1

This is false, because we assumed that (A-B)/(A-B) = 1 in step 5.
However, if A=B, as in 1) then (A-B) = 0
Therefore we have divided 0 by 0 which is not one. Otherwise the proof that 1 = 2 would have worked.

Answer 3

0/1 is equivalent to 0. 1/0 is an undefined term.
Since from the field axioms: one of them states that for every nonzero number, a*(1/a)=1.
if 1/0 = x
=> x*0=1
from this expression, we can't find a value for x such that if we multiply that to 0 will result to 1. Thus, we can say that 1/0 is undefined.
Also 0/0 is also undefined. Since if 0/0=x
=> 0*x=0
from that expression, x can be any number such that if we multiply it to zero the result is zero. That's why 0/0 is also undefined.

Answer 4

A.
Consider 1/0 = x
This implies that x*0 = 1
However, any number muliptled by zero must be zero.
Therefore the premise is not defined.

B.
Consider 0/1=y
This implies that y*1=0
y=0

C.
Consider 0/0=z
This implies that z*0= 0
That means that *any* z appears to satisfy the equation.
However, a/a=1.
And, 1 is not equivalent to all numbers.
Thus there is no defined solution.

Answer 5

1/0=undefined
Proof:0*0≠1
0≠1

0/1=0
0*1=0
0=0

0/0=undefined
Same example as 1/0.

Answer 6

0/1 = 0. 1/0 and 0/0 does not exist. You can't divide by zero. When a limit approaches 1/0, however, it approaches infinity.

Answer 7

1/0=infinity
0/1=0
0/0 is undefined.

Answer 8

1/0= can't divide by zero
0/1= 0
0/0 is an "indeterminate form"
an indeterminate form is an algebraic expression whose limit cannot be evaluated by substituting the limits of the subexpressions.