Thread: Greatest Integer Function

I am slightly confused about this greatest integer function.
For [[5.95]], the answer is 5 "...since 5 the largest integer which is less than or equal to 5.95."

Am I understanding this correctly by saying that the answer is the number in the unit's place. If that is the case, then the answer for [[3.66]] = 3, right?

The textbook tells me that "...negatives are a bit tricky. For [[-1.6]], the answer is -2 not -1."

Can someone explain why the answer is -2 not -1? Also, I need someone to briefly explain how this function is applied in real-life.

Is this function the same as the step function?

What is the easiest way to graph this function?

Originally Posted by sharkman

I am slightly confused about this greatest integer function.
For [[5.95]], the answer is 5 "...since 5 the largest integer which is less than or equal to 5.95."

Am I understanding this correctly by saying that the answer is the number in the unit's place. If that is the case, then the answer for [[3.66]] = 3, right?

The textbook tells me that "...negatives are a bit tricky. For [[-1.6]], the answer is -2 not -1."

Can someone explain why the answer is -2 not -1? Also, I need someone to briefly explain how this function is applied in real-life.

Is this function the same as the step function?

What is the easiest way to graph this function?

Yes for positive numbers it will be the integer ignoring the decimals

[[-1.6]]=-2 since -2 is the greatest integer which is <-1.6, -1 is not <-1.6, so -1 is not the answer

In real life, you probably won't see this function unless to take more math classes or some physics and engineering classes, it can come up (or something similar) in a differential equation

To graph this function, it is the step function that most people think of, it just consists of horizontal lines of length 1 with breaks at the integers