Question

Greatest Integer Function: In defining [[1-3x]], As x->0+, 1-3x->1*-, [[1-]]=0, why is the sign of the 1* negative? How will we know if it is negative or positive?

Answer 1

Also, in defining [[4-x]], how did we come up with 3 and 2? I'm not asking for the solution, just the definition. No solving is needed for these questions.

Answer 2

[x] is the greatest "integer" less than or equal to x

Answer 3

for example
[3.5] = 3

Answer 4

see if you can find [2.88]

Answer 5

@ganeshie8 Yeah I understand how to find the greatest integer function but my professor requires us to define the greatest integer function, and I'm just wondering how to know the sign of 1*? Why is it (-)?

Answer 6

@ganeshie8 Take a loot at the screenshot I posted for a clearer picture of what I'm trying to say.

Answer 7

Yes, can you answer my earlier question

Answer 8

@ganeshie8 2

Answer 9

how about [-5.33] ?

Answer 10

@ganeshie8 -6

Answer 11

great! just making sure :) lets get to the question in attachment

Answer 12

\(x\to 1^{+}\) means you're approaching \(1\) from the right hand side, so let \(x=1.001\) maybe

Answer 13

[1.001] = ?
[4-1.001] = ?

Answer 14

@ganeshie8 1 and 2

Answer 15

thats it!

Answer 16

@ganeshie8 So how about the (-)??