Greatest Integer Function

Section 1.6

See attachment.

Let [[ x ]] = greatest integer function

Why [[ x ]] less than or equal to x?
What exactly does that mean?

I don't quite understand how to evaluate the greatest integer function.

Look at the attachment.

Why does [[ 1/10 ]] = 0?

Why does [[ 1.5 ]] = 1?

Explain attachment.

 

Let [[ x ]] = greatest integer function

Why [[ x ]] less than or equal to x? => means [[ x ]] is a function where you have to find the largest integer that is less than or equal to x

Why does [[ 1/10 ]] = 0? => 1/10 is not an integer, and 0<=1/10<=1, so the largest integer that is less than or equal to x=1/10 is 0

Why does [[ 1.5 ]] = 1? same reason as above: 1.5is not an integer, and 1<=1.5<=2, so the largest integer that is less than or equal to x=1.5 is 1

 

Cool. I will post one or threads in terms of evaluating step functions. As far as graphing by hand, Desmos, wolfram and mathway will do. Graphing by hand is cool but doing the actual algebra work is more important. Take a break. I will be back on Thursday or Friday with more questions, especially evaluating the step function. I must understand how to do before moving on in the textbook. You know, sometimes I feel like going all the way back to Algebra 1 due to frustration. Good night.

 

Check out my thread Evaluating A Step Function.