Math Is Fun Forum

cooljackiec

Member

Registered: 2012-12-13

Posts: 186

Floor functions

{a} denotes the fractional part of a

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I see you have graph paper.
You must be plotting something

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Floor functions

Are you meant to solve it?

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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.

cooljackiec

Member

Registered: 2012-12-13

Posts: 186

Re: Floor functions

Yes

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I see you have graph paper.
You must be plotting something

cooljackiec

Member

Registered: 2012-12-13

Posts: 186

Re: Floor functions

Bump

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I see you have graph paper.
You must be plotting something

Olinguito

Member

Registered: 2014-08-12

Posts: 649

Re: Floor functions

No solution.

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Bassaricyon neblina

Olinguito

Member

Registered: 2014-08-12

Posts: 649

Re: Floor functions

Here's an algebraic proof. For all x,

[list=*]
[*]

[/*]
[/list]

Last edited by Olinguito (2015-03-30 23:43:57)

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Bassaricyon neblina

Bob

Administrator

Registered: 2010-06-20

Posts: 10,803

Re: Floor functions

hi Olinguito

Graph.  Excellent idea.  But I'm puzzled about that proof.  What am I missing?

OK, I like that.

Eh?  x = 2.5 => (FLOOR(x^2)+5)/4 = 2.75 yet x^2 + 1 = 7.25

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Olinguito

Member

Registered: 2014-08-12

Posts: 649

Re: Floor functions

Oops, I did it wrong.

Back to the drawing board.

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Bassaricyon neblina

Olinguito

Member

Registered: 2014-08-12

Posts: 649

Re: Floor functions

Okay, this should work. For all x,

[list=*]
[*]

[/*]
[/list]

because

.

Also, for all x,

[list=*]
[*]

[/*]
[/list]

(Fractional parts cannot be neagative.)

for all x.

Is this better, Bob?

Last edited by Olinguito (2015-03-31 20:04:37)

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Bassaricyon neblina

Bob

Administrator

Registered: 2010-06-20

Posts: 10,803

Re: Floor functions

hi Olinguito

Yes; that looks good to me.

Strictly, as you have one thing ≥ x and another ≥ 0, when you add them you get (one thing + another) ≥ x

But that is easily remedied.

Equality occurs at x = 2, so check what happens there.

(floor(2^2)+5)/4 = (4+5)/4 = 2.25.  So this is the closest you can get to the graphs crossing.  This shows it:

Thanks for the answer.  One wonders why the question was set like this.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Olinguito

Member

Registered: 2014-08-12

Posts: 649

Re: Floor functions

Strictly, as you have one thing ≥ x and another ≥ 0, when you add them you get (one thing + another) ≥ x

No, I have the first thing > x and the other ≥ 0.

Last edited by Olinguito (2015-03-31 04:20:59)

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Bassaricyon neblina

Bob

Administrator

Registered: 2010-06-20

Posts: 10,803

Re: Floor functions

Oh yes.  Didn't spot that.  You're right.    Apologies.    I'm 'ticking' myself off here.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

cooljackiec

Member

Registered: 2012-12-13

Posts: 186

Re: Floor functions

Why did you guys remove {x}

How do u solve this?

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I see you have graph paper.
You must be plotting something

Bob

Administrator

Registered: 2010-06-20

Posts: 10,803

Re: Floor functions

hi cooljackiec,

{x} = x^2 - floor(x^2), so it has not been lost.  This is simply a way to graph the left hand side of the equation using available functions.

{fractional part} = <whole> minus <integer part>.

Olinguito has shown that you cannot find values of x to fit this equation.  The solution is "no values".

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Olinguito

Member

Registered: 2014-08-12

Posts: 649

Re: Floor functions

Why did you guys remove {x}

Sorry, it was a typo. I've put it back in post #9.

Last edited by Olinguito (2015-03-31 20:09:15)

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Bassaricyon neblina