Approaching Zero

Calculus Level 2

x0.10.010.0010.00010.00001x00000 \boxed{\begin{array}{c|r:r:r:r:r} x & 0.1 & 0.01& 0.001& 0.0001& 0.00001\\ \hline \lfloor x \rfloor & 0 & 0 & 0 & 0 & 0 \end{array}}

By looking at the table above, is it true that as xx approaches 0, then x\lfloor x \rfloor approaches 0 as well?
That is, is limx0x=0 \displaystyle \lim_{x\to0} \lfloor x\rfloor = 0 correct?

Notation: \lfloor \cdot \rfloor denotes the floor function.

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