OK, hear me out. Imagine if we made a number really, really small. Like imagine a small number, but smaller than that.

Now, this number is not zero, but it's so small that if you squared it, it would become zero.

What do you think?

e != 0
e * e = 0
e = 0 / e = 0

don't work, yo. you'll need to propose variations on arithmetic operations. what ever you come up with (assuming what you propose is consistent), it won't be a field or act like one.

>>16733184 (OP)
That's not how it works, retard.

>>16733184 (OP)
You can do so. It has been done.

>>16733184 (OP)
op is testing whether sci has heard about dual numbers.

>>16733184 (OP)
tis called dual numbers

ITT: people getting filtered by non-Archimedean fields.

>>16733184 (OP)
Based. Sounds like it has applications in perturbative physics, specifically pQCD

>>16733361
Yes, quantum is full of such hacks to make it work.

>>16733328
Fields don't have zero-divisors, dickhead.

>>16733184 (OP)
So it's a positive number. Might as well be 100.

>>16733382
Keyword was "non-Archimedean" anyway, not field, retard.

>>16733328
if it has nilpotents it ain't a field

>>16733382
>you can't divide by zero because... umm... you just can't, ok?
>no, you're not allowed to compile an internally-consistent set of grammatical, syntactic, and logical rules that turn division by zero into a meaningful mathematical operation... because... ummm... YOU JUST CAN'T, OKAY?
I bet you also believe the moon landing never happened because heavier-than-air flying machines are physically impossible.

>>16733184 (OP)
I saw this in a taylor series, it's not a novel idea

>>16733430
Nobody mentioned division by zero, you sped.
>>16733415
A non-archimedean field is a field, smoothbrain.

>>16733415
i was first to respond, and i considered non-archimedean fields, however the definition for those does not use 0, which is a special and unique number in a field. therefore, what OP is asking isn't the same as considering if a field is archimedean or not. the litmus test for an archimedean field is that there exists a number n such that x * n > y for any x and y, which is very different than asking if you square a number it gives you 0.

>>16733430
zero divisors are niggas a & b that when multiplied equal zero yet neither a or b are zero, you retard, & what's worse you just made the projective & affinely extended reals sound rely fucking faggy, do better

>>16733328
rings. not fields, rings.

>>16733591
ah, i haven't studied rings nearly as much as groups and fields

congratulations! you're doing math like a physicist

>>16733437
>Nobody mentioned division by zero, you sped.
Then what did the anon they replied to mention >>16733382?

>>16733184 (OP)
>a number really, really small. Like imagine a small number, but smaller than that.
So an infinitesimal?

>>16734033
Zero-divisors.

>>16734053
Then what is the division by in that case, if not zero?

Soooo, smaller than 0 but not negative?

>>16734062
wait im retarded i forgot how fractions work

[math]\mathcal{DOWN SYNDROME} [/math]

>>16734061
faggot >>16733525