I have a question, if is a sequence of all rational numbers, let

why do we have the following inclusion ?

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- Oct 9th 2013, 10:23 AMraymanrationals and union of intervals that covers it
I have a question, if is a sequence of all rational numbers, let

why do we have the following inclusion ? - Oct 9th 2013, 10:27 AMemakarovRe: rationals and union of intervals that covers it
Himm, if x ∈ A and y ∈ B, is it clear to you that {x, y} ⊆ A ∪ B?

- Oct 9th 2013, 10:34 AMraymanRe: rationals and union of intervals that covers it
yes it is, but I still don't understand the inclusion. Each of is a set (closed interval) containing infinitely many rational numbers bounded by the end points of each interval. Will their union include all rationals?

- Oct 9th 2013, 10:45 AMemakarovRe: rationals and union of intervals that covers it
- Oct 9th 2013, 10:51 AMraymanRe: rationals and union of intervals that covers it
Ah yes of course, I got it:) thank you

- Oct 9th 2013, 10:55 AMPlatoRe: rationals and union of intervals that covers it