What if we define 1 to be 0?
Do you mean that 1 becomes 0 or that 0 becomes one ?
Then for every number a, a=a*1=a*0=0.
In other words, all numbers are the same, which is a pretty boring system to work in.
>>8149902
Ok. Why don't we make a new value for division by 0, like i was invented for sqrt(-1)?
>>8149904
I'll call it [math]\infty[/math], it equals its opposite but is not 0
>>8149904
They exist and they're called Wheels. Extending an algebra to a wheel changes the properties of division. This is different from adding the imaginary unit, because the complex numbers still behave "like" the real numbers in most ways (you can multiply, divide, etc.)
>>8149904
There are of course a million mathematical theories. Those which turn out not useful are not taught
One that's used (e.g. in measure theory), which extends the real number line, is
https://en.wikipedia.org/wiki/Extended_real_number_line#Algebraic_properties
Also consider
https://en.wikipedia.org/wiki/Hyperreal_number
If you make sense of x/0, you must always fix stuff on one end or another, so those theories are always much more complicated than standard arithmtic
What if we define your mom to not be a whore?
>>8149979
That's a contradiction.
>>8149979
Based on the Axiom that OP is a faggot, the proof that his mother is a whore follows trivially.
>>8149899
What if we define OP not to be gay?
>>8149899
1=0, as in the additive identity = the multiplicative identity, can only be satisfied in the trivial ring with 1 element.
>>8149899
Something like this.
https://en.wikipedia.org/wiki/Field_with_one_element
>>8150028
Kek
>>8149899
Then everything = 0. Mathematically this is sound. But, the result is a system that is practically useless.
