anonymous
  • anonymous
help please see below
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
the set of integers as \[\mathbb{Z}^- {....-3,-2,-1,0,1,2,3....}\] the greatest integer of x is denoted as \[\lfloor x \rfloor\] is defined to be the largest interger k with \[k \le x\] discuss with your classmates how \[\lfloor x \rfloor\] may be described as a piecewise defined function
anonymous
  • anonymous
also is \[\lfloor a+b \rfloor = \lfloor a \rfloor+\lfloor b \rfloor\] always true? what if a or b was an integer? test some values make a conjecture and explain your result
anonymous
  • anonymous
@DebbieG or @Directrix

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DebbieG
  • DebbieG
You'll gain a better understanding of this function if you look at some of the values of it. \(\lfloor 3 \rfloor=3\) \(\lfloor 3.2 \rfloor=3\) \(\lfloor 3.8 \rfloor=3\) \(\lfloor 3.9999 \rfloor=3\) \(\lfloor 4 \rfloor=4\) So, for example \(\lfloor x \rfloor=3\) for \(3\le x <4\) Now think about extending that idea over the whole set of integers, and you should see this as a piecewise function. For the 2nd question, try some values and see if \(\lfloor a+b \rfloor = \lfloor a \rfloor+\lfloor b \rfloor\). E.g., compare \(\lfloor 4 \rfloor+\lfloor 5 \rfloor\) to \(\lfloor 4+5 \rfloor\) \(\lfloor 4.9 \rfloor+\lfloor 5.9 \rfloor\) to \(\lfloor 4.9+5.9 \rfloor\)

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