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:

Pilot Project

An initial small-scale implementation that is used to test the feasibility, duration, cost, risk, and adverse effects of a project or innovation.

Scientific Inquiry

The process of exploring the natural world through observation, experimentation, and data analysis to answer questions.

Comparative Reasoning

A method of thinking where different objects, ideas, or situations are examined in relation to each other to identify similarities and differences.

Ideological Reasoning

Making conclusions or judgments based on a set of beliefs or ideologies.