Defining Division by zero,seems flawed
I'm very interested in the number 0
And I was not very satisfied when divison of zero is undefined (except in projective geometry, but the "division sign" does not mean the division in a simple sense)
One day I came up with this
Given
0N=0 ---(*) (where N is any real number)
(But we will consider N=0 separately below unless specified as it seemed to does not work)
If we define a new relation (0[sup]-1[/sup]) which act as the inverse of "multiplied by 0" (Note 0[sup]-1[/sup] =/= 1/0), then the above becomes
N=0[sup]-1[/sup] ---(1)
Now given
0/N=0 (where N is any real number) ---(2*)
(However unless specified, we only consider N=/=0)
(0)(1/N)=0
Since 1/N=/=0, it is just a constant
Using (1), it now becomes
1/N=0[sup]-1[/sup] ---(2a)
Furthermore using (1)
Therefore (1)=(2a)
and ()
Therefore I get two bizarre results
1/N=N
1/0[sup]-1[/sup])=0[sup]-1[/sup])
(N=/=0)
Now consider
1/0
By (*) we get
1/0=1/0N
=(1/0)(1/N)
Using (3), it now becomes
(1/0)(N)
=N/0
Therefore another bizarre result
1/0=N/0---(4)
Since N is any real number therefore
1/0=2/0=3/0=1.5/0=root(2)/0 ... EXCEPT 0/0
Now consider when N=0 in (*), i.e.
(0)(0)=0
Using the relation invented in (1)
0=0[sup]-1[/sup] (N=0) ---(5)
Unfortunately, I still get nowhere when dealing with 0/0
0/0
=0(1/0)
Using (4)
=0(N/0)
When N=0
Using (5)
=0[sup]-1[/sup](N/0[sup]-1[/sup])
For Tl;dr
Red means some possibly flawed steps and green means steps that are proved true (NOTE if one step is flawed that means the subsequent steps are also flawed, however I only highlighted the steps that seemed to assume something)
Please tell me what's wrong in this "proof" and debunk if necessary
I'm very interested in the number 0
And I was not very satisfied when divison of zero is undefined (except in projective geometry, but the "division sign" does not mean the division in a simple sense)
One day I came up with this
Given
0N=0 ---(*) (where N is any real number)
(But we will consider N=0 separately below unless specified as it seemed to does not work)
If we define a new relation (0[sup]-1[/sup]) which act as the inverse of "multiplied by 0" (Note 0[sup]-1[/sup] =/= 1/0), then the above becomes
N=0[sup]-1[/sup] ---(1)
Now given
0/N=0 (where N is any real number) ---(2*)
(However unless specified, we only consider N=/=0)
(0)(1/N)=0
Since 1/N=/=0, it is just a constant
Using (1), it now becomes
1/N=0[sup]-1[/sup] ---(2a)
Furthermore using (1)
Therefore (1)=(2a)
and ()
Therefore I get two bizarre results
1/N=N
1/0[sup]-1[/sup])=0[sup]-1[/sup])
(N=/=0)
Now consider
1/0
By (*) we get
1/0=1/0N
=(1/0)(1/N)
Using (3), it now becomes
(1/0)(N)
=N/0
Therefore another bizarre result
1/0=N/0---(4)
Since N is any real number therefore
1/0=2/0=3/0=1.5/0=root(2)/0 ... EXCEPT 0/0
Now consider when N=0 in (*), i.e.
(0)(0)=0
Using the relation invented in (1)
0=0[sup]-1[/sup] (N=0) ---(5)
Unfortunately, I still get nowhere when dealing with 0/0
0/0
=0(1/0)
Using (4)
=0(N/0)
When N=0
Using (5)
=0[sup]-1[/sup](N/0[sup]-1[/sup])
For Tl;dr
Red means some possibly flawed steps and green means steps that are proved true (NOTE if one step is flawed that means the subsequent steps are also flawed, however I only highlighted the steps that seemed to assume something)
Please tell me what's wrong in this "proof" and debunk if necessary
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