Modeling a greatest integer function. I'm trying to model a function that resembles a greatest integer function. The domain is from [0, infty). The inputs from 0 to 1.5 (non-inclusive) need to be mapped to an output of 0, and 1.5 to infty mapped to 1. But, I'm trying to not use a piecewise function. Is it possible to accomplish this?

Aliyah Thompson

Aliyah Thompson

Answered question

2022-11-17

Modeling a greatest integer function
I'm trying to model a function that resembles a greatest integer function. The domain is from [0, ). The inputs from 0 to 1.5 (non-inclusive) need to be mapped to an output of 0, and 1.5 to mapped to 1. But, I'm trying to not use a piecewise function. Is it possible to accomplish this?
Here's what I've tried:
f ( x ) = x 1.5

Answer & Explanation

hoatryearnenizts

hoatryearnenizts

Beginner2022-11-18Added 10 answers

Explanation:
Try this function,
| x 1.5 | 2 x 3 + 1 2
Although this is very artificial, it works.
charmbraqdy

charmbraqdy

Beginner2022-11-19Added 4 answers

Step 1
Your input mapping is currently ambiguous: do you mean to send 1.5 to 0, or 1?
Step 2
Using a characteristic function:
1 χ [ 0 , 1.5 )
where χ A ( x ) takes the the value 1 if x A and 0 otherwise.

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