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## Homework Statement

"If x is a real number, show that there exists a Cauchy sequence of rationals Xl, X2,... representing X such that X n < x for all n."

## Homework Equations

- All Cauchy sequences are convergent

- All Cauchy sequences are bounded.

## The Attempt at a Solution

These proofs that involve Cauchy sequences have been rough on me, and I'm trying to start working through them rather than just hunting for solutions.

But I just don't know quite where I should start. What should I be assuming or trying to show? Do I start with a series where Xn<X for all n that converges to x and show it's Cauchy? Just kinda stumped so far :/