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#1 2016-03-05 14:08:11

cooljackiec
Member
Registered: 2012-12-13
Posts: 186

Functions

ANMpLHq.jpg

I am a little confused on this notation and what it means? more specifically what does it mean N->N

and also what does it mean on the line with: g(n+1)-g(n)

Last edited by cooljackiec (2016-03-05 14:09:57)


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

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#2 2016-03-05 15:42:22

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: Functions

Hej!

g:N->N means that g maps natural numbers into natural numbers.

And

means that the images of n and n+1 differ by one. For example, if g(13)=3, then g(14) can be either 2 or 4.

Last edited by anonimnystefy (2016-03-05 15:42:54)


“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.

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#3 2016-03-07 16:36:38

cooljackiec
Member
Registered: 2012-12-13
Posts: 186

Re: Functions

thanks for the clarifications.
I'm confused on how you found the answer to a.

g(2015) is close to g(2016)=g(672)=g(224). g(224) is close to g(225)=g(3)=g(1). So g(2015) maximum seems to be g(1)+2. So is the answer not 3?


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

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#4 2016-03-07 19:02:40

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: Functions

Why should g(225)=g(3)?


“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.

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#5 2016-03-08 15:40:59

cooljackiec
Member
Registered: 2012-12-13
Posts: 186

Re: Functions

oh i see i messed up calculations. How exactly can you find b though?


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

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#6 2016-03-09 10:36:00

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,049

Re: Functions

Well, the first thing is to notice a pattern and conclude that you get maximum values of g when it satisfies the following:


With the initial conditions of
and
.
From here, we can see that if n is the first number for which g(n)=m, then 3n-1 is the first number for which g(3n-1)=m+1. So, if I call
the first number for which
, then

Now you can solve this recurrence and see what you get for m=2015. smile

Last edited by anonimnystefy (2016-03-09 10:37:04)


“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.

Offline

#7 2016-03-10 15:22:04

cooljackiec
Member
Registered: 2012-12-13
Posts: 186

Re: Functions

thanks a lot smile


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

Offline

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