>>13234882proposal - "0" just means the zero set, and contains the infinitesimals.
The same way you'd say for any real x, or for complex numbers, for any infinitesimal you would say
Likewise, for any infinite-magnitude values, you would say
That way, you could argue both 0 and on their own are undefined - the same way a negative sign is undefined without a magnitude associated with it. You may not know exactly which infinitesimal/infinite they are. But you know the element you're calling "0" actually exists, and is an element in a set, and if the infinitesimal is well defined, paradoxes like
>>13234925 don't need to occur.