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#1 2012-11-20 20:02:23

princess snowwhite
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value of function

f(x)= [x] + (x-[x])^2.
where [x] means largest integer not exceeding x.
then find set of all values taken by f

#2 2012-11-21 03:35:57

princess snowwhite
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Re: value of function

I think the set will be infinite. does anyone has anything else in mind?

#3 2012-11-21 03:40:27

zetafunc.
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Re: value of function

Is [x] the floor function, then? (e.g. [6] = 6?)

#4 2012-11-21 04:01:03

princess snowwhite
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Re: value of function

yes for n=2, [n]=2 but when n=1.6, [n]=1

#5 2012-11-21 04:07:19

zetafunc.
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Re: value of function

Then, I think f can take on any real value.

#6 2012-11-21 04:12:54

princess snowwhite
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Re: value of function

so I smile. the set should be infininte

#7 2012-11-21 05:21:57

anonimnystefy
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Re: value of function

zetafunc. wrote:

Then, I think f can take on any real value.

That is true. You can even plot it to see that the range is R (ie. the reals).


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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