Word Count : 431

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(a) False. The set is meant to be $\{x\in\mathbb{R}: x^{2}-3x+2=0\}$. Factoring gives $(x-1)(x-2)=0$, so the real solutions are $x=1$ and $x=2$ only. Hence the solution set contains exactly two elements and is therefore finite, not infinite. In calculus terms, the quadratic polynomial intersects the $x$-axis at two points; there is no continuum of roots, so the zero set cannot be infinite. (b) False. The greatest integer (floor) function $\lfloor x\rfloor$ is piecewise constant with jumps at every integer. For any noninteger $x$, there exists an open ___ _________ _________ ______ ________ _______ ___ ____ ______ _________ ___ ________.
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