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Where do these go? abs[1.5] abs[0.5] abs[-0.5] abs[-1.5]
first off, what do they mean by the greatest integer function
That's what I was asking. There are various definitions. Often it is the "Greatest Integer NOT GREATER THAN the given value" Therefore: abs[1.5] = abs(1) = 1 abs[0.5] = abs(0) = 0 abs[-0.5] = abs(-1) = 1 abs[-1.5] = abs(-2) = 2 Make sense?
but 1.5 is greater than 1
also i thought decimals are not integers
The Domain of this function is ALL Real Numbers. The Range is quite a different animal. The Greatest Integer function takes ANY argument but produces only integers. This, 1.5 can go into this function (no one cares if it's an integer), but you cannot get it out (it's not an integer).
what does the graph look like
and so how do we find the range
You tell me.  = 0 [0.1] = 0 [0.2] = 0 [0.4] = 0 [0.8] = 0 [0.9] = 0 [0.99] = 0 [0.999] = 0 [0.9999] = 0 [0.99999] = 0  = 1
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so is it just points on a graph
and range is just 0 and 1 and 2 and (no negatives)
No, it's mostly continuous. I just picked a few points between 0 and 1 to provide an example of it;'s behavior. Once you hit an integer, it jump to that integer and stays there until you hit the next integer.
can u draw it please
i am having trouble understanding you
It is a series of horizontal line segments. Start at (0,0) and proceed to (1,0). Traditionally, one uses a closed dot at (0,0) and an open circle at (1,0). Then it jumps to a closed dot at (1,1) and continues horizontally to an open dot at (2,1)
can you please draw it for me
Are you saying you cannot draw a horizontal line from (0,0) to (1,0)?
|dw:1378190001583:dw| The closed circles on the left and closed on the right are missing, but that's the idea.
Whoops! OPEN on the right.