Let A be the set of real numbers x such that 0<x<=1. For every x element of A, let E sub x be the set of real numbers y such that 0<y<x. Then(adsbygoogle = window.adsbygoogle || []).push({});

for x in A the intersection of all Esubx is empty.

I do not understand that the intersection is empty. I see that my index set is infinite and that as x approaches zero the magnitude of the sets Esubx become infinitely small so that the intersection is not abtainable but does that mean it is non-exisitant?

Rudin suggests I note that for every y>0, y not in Esubx if x<y. Hence y not in the insection of all Esubx. I have a problem understanding this suggestion. My index set is bounded above and and not bounded below. It seems to me that y could be greater than or equal to x but not just greater than x. Vastly confused?!??!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Need help understanding this problem

**Physics Forums | Science Articles, Homework Help, Discussion**