Talk:Continuous or discrete variable

a flawed and clumsy definition

begin quote:

In mathematics, variables are either continuous or discrete, depending on whether or not there are gaps between a value that the variable could take on and any other permitted values.

end quote
Really? If a variable can assume any value except 0, then that's a gap. Does that make it discrete? Michael Hardy (talk) 14:52, 30 April 2015 (UTC)[reply]

. . . and notice the two alternatives:

"whether"
"or not".

Which corresponds to "continuous" and which to "discrete"? If the reader thinks there's a tacit "respectively" then the first would be "continuous" since "continuous" was named before "discrete" in the opening sentence. Michael Hardy (talk) 15:12, 30 April 2015 (UTC)[reply]

The article later has "the number of permitted values is either finite or countably infinite" for discrete. That seems more rigorous. Common objection is, typical motivating examples of continuous variables are time and other physical measurements. Common reply is, we can usefully model them as uncountable, without claiming the model is literally true to actual infinity. --GodMadeTheIntegers (talk) 15:52, 30 April 2015 (UTC)[reply]

I don't really think much of this kind of article in general, and the lack of references makes it especially problematic from the standpoint of WP:OR. But if I were pressed to do so, I would probably summarize the distinction between continuous and discrete variables as follows:

In mathematics, a variable is continuous if it assumes values in a continuum (such as an interval), and discrete if it assumes values in a discrete space (such as the integers or a more general lattice).

We do not need to reinvent the wheel here. Sławomir Biały (talk) 16:03, 30 April 2015 (UTC)[reply]