Math Is Fun Forum

cooljackiec

Member

Registered: 2012-12-13

Posts: 186

Functions

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)

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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: 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)

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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: 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?

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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: Functions

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

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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: Functions

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

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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: 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.

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

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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: Functions

thanks a lot

---

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