Mathematicians who are finitists.

[polymath257]

@polymath257 what is the english name of this axiom: "Consider two convergent sequences A(n), B(n) with n belonging to the natural numbers and a sequence of intervals where [A(n), B(n)] is a superset of [A(n+1),B(n+1)] for all n. Then, there exists one and only one real number c that belongs to all the intervals, same as saying the intersection of these intervals is not an empty set"

I really dunno the english name for this.

It is one of the many results due to Cantor and often carries his name.

Some care is required, however. As stated, the hupotheses show the intersection is non-empty, but they do NOT show that there is only one point in common to all. For that, you need, in addition, that B(n)-A(n)-->0.

For example, if A(n)=-1/n and B(n)=1+(1/n), then the intervals [A(n),B(n)] satisfy your hypotheses, but the intersection is the whole interval [0,1].

The result you stated is usually associated these days with compactness and it is in the subject of topology that it gets its full expression.