Math Is Fun Forum

juantheron

Member

Registered: 2011-10-19

Posts: 312

greatest integer

Show that

where

greatest integer

anyone have any idea how can i prove that

Thanks

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: greatest integer

Hi;

Is there some bounds on n?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

juantheron

Member

Registered: 2011-10-19

Posts: 312

Re: greatest integer

n is a natural number  including zero

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: greatest integer

hi bobby

have you found a solution?

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: greatest integer

Yes, but it is not a proof,

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: greatest integer

nevermind.i would like to see it.

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: greatest integer

It ain't nothing but some scribblings and a wild guess or two. Not fit for the public yet.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

juantheron

Member

Registered: 2011-10-19

Posts: 312

Re: greatest integer

actually bobbym  here

is a positive Integer

in my book it is given that if

Then prove that 

Now  How can i prove 

Last edited by juantheron (2012-01-14 04:49:37)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: greatest integer

Hi juantheron;

Just curious, what book?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: greatest integer

hi juan

maybe you could take two cases:
1.) x=2k
[x/2]=[k]=k
and
[(x+1)/2]=[(2k+1)/2]=[k+1/2]=k

so their sum is k+k=2k=n

2.x=2k+1
[x/2]=[(2k+1)/2]=[k+1/2]=k
and
[(x+1)/2]=[(2k+2)/2]=[k+1]=k+1

so their sum is k+k+1=2k+1=x

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

TheDude

Member

Registered: 2007-10-23

Posts: 361

Re: greatest integer

I'm not sure how robust this is but I think you can do it with induction.

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Wrap it in bacon

juantheron

Member

Registered: 2011-10-19

Posts: 312

Re: greatest integer

to bobbym book = text book of differential calculus

juantheron

Member

Registered: 2011-10-19

Posts: 312

Re: greatest integer

Thanks Dude.