Prove or Disprove: for All Positive Real Numbers $x$ And $y$ $\lfloor x \cdot y \rfloor \leq \lfloor x \rfloor \cdot \lfloor y \rfloor$

question 157

Essay

Prove or disprove: For all positive real numbers $x$ and $y$ , $\lfloor x \cdot y \rfloor \leq \lfloor x \rfloor \cdot \lfloor y \rfloor$

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Definitions:

Dialectical Behavior Therapy

A type of cognitive-behavioral therapy that emphasizes balancing acceptance and change in treating emotional disorders.

Cognitive-behavioral Therapy

A form of psychotherapeutic treatment that aims to change patterns of thinking or behavior that are behind people's difficulties, and so change the way they feel.

Suicidal Behavior Patterns

Patterns of behavior that can lead to attempts or completed suicide, including verbal hints, giving away possessions, and previous attempts.

Virtual Reality Exposure

A therapeutic technique using virtual reality technology to expose individuals to stimuli related to their fears or disorders.