Convergent Sequence of Rationals
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Show that, for every real number y, there is a sequence of rational numbers which converges to y.
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Solution Summary
A detailed proof of the following statement is given: For every real number y, there is a sequence of rational numbers which converges to y.
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There are two cases to consider:
Case i. y is rational
For every n >= 1, let a_n = y - (1/n). Then a_n is rational for every n >= 1, since (a) both y and 1/n are rational and (b) the difference of two rational numbers is rational. Clearly, the sequence {a_n} converges to y.
Example: y = 3.
The sequence of rational ...
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