On 23 Mrz., 21:26, William Hughes <wpihug...@gmail.com> wrote: > > > > > I say that there is no finite line that changes the union. > > > > Correct > > > > > So the union would be the same if there was no finite line. > > > > Nope, does not follow.
In set theory we can construct the set of all elements that have a certain property. Does that mean that the property vanishes if too many elements belong to the set? The set of all negative numbers cannot be subtracted from the real line without subtracting also a positive number ? The set of all red cars cannot be formed without containing a green car too? The set of all lines without any relevance for the union cannot be subtracted without changing the union? > > > It follows in ordinary logic. The negation of "no finite line changes > > the union" is "at least one finite line changes the union". > > True but irrelevant.
You claim that no finite line of the set changes the union. You claim that when every finite line which does not change the union, is deleted, then the union is changed. So you claim just what you acknowledge as true, namely the proposition, and you claim its negation. Why should it be irrelevant?