## the boundary of set of rational number is

Theorem: A set A ⊂ X is closed in X iﬀ A contains all of its boundary points. Step 3: Use the boundary point (s) found in Step 2 to mark off test intervals on the number line. n be an ordering of the rational numbers, then {s n} n=1 ∞ =Q 4. The ancient greek mathematician Pythagoras believed that all numbers were rational, but one of his students Hippasus proved (using geometry, it is thought) that you could not write the square root of 2 as a fraction, and so it was irrational. Adding 4 and 4 gives equals the natural number 8 and multiplying 5 by 1,000,000 equals the natural number 5,000,000. (a;b] is the set of all real numbers xwhich satisfy a

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