Sine Spe (Without hope.)


(pronounced: S-ee-N-ay S-p-ay)

Venezuela. To spell it out, you say:

V (OObay) E (ay) N (Enay) E (ay) Z (thAYta) U (OObay) E (ay) L (EHlay) A (ah)

Mill - n

Like a wind-mill with a soft n.

Context: Scottish surname, lived in Scotland for 7 years.

That's called a tilda. Spanish uses it. It makes the standard N sound (n-ay) more like a N-Y sound. (n-yay)

Let (an) be a convergent sequence in metric space X. Let "a" be the limit of an. Then for sufficiently large N, if x,y>N, d(ay,a)<e/2 and d(ax,a)<e/2 for any e greater than zero.

We add these inequalities and get d(ay,a) + d(ax,a)<e. But by the triangle inequality d(ay,ax)<d(ay,a) + d(ax,a), so

d(ay,ax)<e for all x,y>N.

(some of those < should be less than or equal to, but it doesn't really affect the proof.)