The set Q is an extension of N, and R in turn is an extension of Q The next few

Question

The set Q is an extension of N, and R in turn is an extension of Q The next few results indicate how N and Q sit inside of R Given any number there exists an satisfying n > x any real number y > 0, there exists an satisfying l/n

Explanation / Answer

Proof of (i) =>(ii) given y>0. from (i), there exists a natural number N s.t. N > 1/y since both y and N are positive, y> 1/N. hence proved. Proof of (ii) =>(i) given x belongs to R if x 0. hence 1/x >0 now from part (ii), we have a natural number M such that 1/M < 1/x hence M > x since both x and M are positive. hence proved. feel free to ask doubts.. PLEASE RATE MY ANSWER FIRST AND REWARD.. THANKS :)

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