Proof: Suppose r and s are rational numbers. If r+s is rational, then by definition of...

Transcribed Image Text:

"Proof: Suppose r and s are rational numbers. If r+s is rational, then by definition of rational r +s a/b for some integers a and b with b0. Also sincer and s are rational, r=i/j and s m/n for some integers i, j, m, and n with j 0 and n0.It follows that m r+s j п which is a quotient of two integers with a nonzero denomi- nator. Hence it is a rational number. This is what was to be shown." "Proof: Suppose r and s are rational numbers. If r+s is rational, then by definition of rational r +s a/b for some integers a and b with b0. Also sincer and s are rational, r=i/j and s m/n for some integers i, j, m, and n with j 0 and n0.It follows that m r+s j п which is a quotient of two integers with a nonzero denomi- nator. Hence it is a rational number. This is what was to be shown."