Prove or disprove: For all real numbers x and $$y , \lfloor x + \lfloor x \rfloor \rfloor = \lfloor 2 x \rfloor$$

Name: Prove or disprove: For all real numbers x and \[y , \lfloor x + \lfloor x \rfloor \rfloor = \lfloor 2 x \rfloor\]
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Question

Quizplus · Accepted Answer

The statement is false because the floor function does not distribute over addition in this way. For example, if x = 0.5, then $\lfloor x + \lfloor x \rfloor \rfloor = \lfloor 0.5 + 0 \rfloor = \lfloor 0.5 \rfloor = 0$, but $\lfloor 2x \rfloor = \lfloor 1 \rfloor = 1$.

Prove or Disprove: for All Real Numbers X And y,⌊x+⌊x⌋⌋=⌊2x⌋y , \lfloor x + \lfloor x \rfloor \rfloor = \lfloor 2 x \rfloory,⌊x+⌊x⌋⌋=⌊2x⌋

Prove or Disprove: for All Real Numbers X And $y , \lfloor x + \lfloor x \rfloor \rfloor = \lfloor 2 x \rfloor$