> binom.test(11,n=24, alternative = "two.sided")

	Exact binomial test

data:  11 and 24
number of successes = 11, number of trials = 24, p-value = 0.8388
alternative hypothesis: true probability of success is not equal to 0.5
95 percent confidence interval:
 0.2555302 0.6717919
sample estimates:
probability of success 
             0.4583333 

Probably not. Or at least we can’t conclude that from the data. ¯\_(ツ)_/¯

I didn’t know that Rómendacil II was born with another name. Got the rest. :)

Logicians are mathematicians. Well, most of them are.

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.

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 countably 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.

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.

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