holomorphic

@holomorphic@lemmy.world

• ⁨Comment⁩ on ⁨Zero to hero⁩ ⁨⁨6⁩ ⁨months⁩ ago⁩:

  Logicians are mathematicians. Well, most of them.

• ⁨Comment⁩ on ⁨Zero to hero⁩ ⁨⁨6⁩ ⁨months⁩ ago⁩:

  I have yet to meet a single logician, american or otherwise, who would use the definition without 0.

  That said, it seems to depend on the field. I think I’ve had this discussion with a friend working in analysis.

• ⁨Comment⁩ on ⁨Explain yourselves, comp sci.⁩ ⁨⁨6⁩ ⁨months⁩ ago⁩:

  But the vector space of (all) real functions is a completely different beast from the space of computable functions on finite-precision numbers. If you restrict the equality of these functions to their extension ,defined as f = g iff forall x\in R: f(x)=g(x), then that vector space appears to be not only finite dimensional, but in fact finite. Otherwise you probably get a countable infinite dimensional vector space indexed by lambda terms (or whatever formalism you prefer.) But nothing like the space which contains vectors like F_{x_0}(x) := (1 if x = x_0; 0 otherwise) where x_0 is uncomputable.

• ⁨Comment⁩ on ⁨Explain yourselves, comp sci.⁩ ⁨⁨6⁩ ⁨months⁩ ago⁩:

  Functions from the reals to the reals are an example of a vector space with elements which can not be represented as a list of numbers.

• ⁨Comment⁩ on ⁨STEM⁩ ⁨⁨8⁩ ⁨months⁩ ago⁩:

  It may have nothing to do with categorization, but has everything to do with categorification which is much more interresting anyway.