(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

1.Given a set T we say that T serves as anindex setfor family F={A_{a}} of sets if for every a in T there exists a set A_{a}in family F.

2. By the union of the sets A_{a}, where a is in T, we mean the set

{x l x[tex]\in[/tex]A_{a}for at least one a in T}. We shall denote it by [tex]\bigcup[/tex](_{a[tex]\in[/tex]T}) A_{a}.

i think its better if i show example

example:

if S is the set of real number, T is the set of rational number, let, for

a[tex]\in[/tex]T, A_{a}= {x[tex]\in[/tex]S l x[tex]\geq[/tex]a}

so [tex]\bigcup[/tex](_{a[tex]\in[/tex]T}) A_{a}= S

what i dont understand

i can see how ..,A_{-1}, A_{0}, A_{1},... is,

and i dont know how to change it to

[tex]\bigcup[/tex](_{a[tex]\in[/tex]T}) A_{a}

or how it is equal to S, because im perplexed with definition (2) particularlyx[tex]\in[/tex]A_{a}for at least one a in T

help help

p/s: sorry if it is abit messy, still progressing in latex

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# Sets definiton

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