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@SolomonZelman you free? :)

do you know how the greatest integer function is defined?

Mm I know what the graph of it looks like. But not quite sure how it's defined

greatest integer function = floor function

think of the number line written vertically
|dw:1444263692393:dw|

approaching it from either the positive or negative side we always do that?

let's try an example
if f(x) = [[x]], then what is f(8.3125) equal to?

8?

yes, how about f(8.99999)

8 still

good, so if the number is positive, you just chop off the decimal portion

now let's try f(-2.462)

Would that round up? to 3?

I think you meant -3

look back to the vertical number line

yes yes sorry o.o

|dw:1444264095476:dw|

so approaching -2
from the right = -2
and from the left = -2 ?

because there's no decimals o.o

look at the rules SolomonZelman posted

Ahh ok.
Approaching - 2 from the right = 2
approaching - 2 from the left = ...1?

idk how you jumped from -2 to +2

*-2
and -3

\[\Large \lim_{x \to -2^{+}} [[x]] = -2\]
\[\Large \lim_{x \to -2^{-}} [[x]] = -3\]
looks good

Sorry, my brains are not working haha =.=

does \[\Large \lim_{x \to -2^{}} [[x]]\] exist?

and then as x approaches -2.4 it = -3

No, it doesn't.

why not?

because the points aren't meeting

so 51(a)(ii) does not exist

ahh gotcha. Okay!

Part b!

for c) the answer is: for all non-integer values of a, yeah?

`for c) the answer is: for all non-integer values of a, yeah?`
agreed

part b) is very similar to what SolomonZelman wrote out

Okay, I wasn't sure if that was too "simple"
So b:
i) n-1
ii) n

looks good

Thank you so much :)

sure thing

hahah my next problem is that! i'll tag you in it ;)

Though from all you said here I think I could get it.