# Homework Help: Property of a sequence for a function.

1. Aug 20, 2011

### AkilMAI

Ok so the ideea of the proble is the following.F:A->B....where A={1...k} and B={1...n}.The problme is divided in 2 parts.
The first part of the problem asked me to write in terms of k and n the formulas for the number of functions,number of injective functions,number of increasing functions...etc.I've done that.What I don't understand is part 2 because the description is confusing for me.
Part two states the following:"For each of the type of functions from part a) describe the coresponding property of the sequence {f(1),......,f(k)} for a function f of that type."
Does this mean to show what it means to be a function,then an injective function and an incresing function and so on?
Appologies if this question is ridiculous.

2. Aug 20, 2011

### micromass

Yes, they're just asking you to say what it means to be injective, increasing, etc. But you must phrase it in such a way to have a statement about {f(1),...,f(k)}.

For example, you could say that f is injective if f(a)=f(b) implies that a=b. But that is not a statement about {f(1),...,f(k)}. The statement we're looking for is that {f(1),...,f(k)} are k distinct values.

3. Aug 20, 2011

### AkilMAI

Can I say the following?
Let A={1...k} and B={1...n} then a function is defined as:f(A):={f(a)|a belongs to A}
And for injective functions f(a)=F(b) if a=b
or should I just say that f(1)=......=F(k) if 1=....=k

4. Aug 20, 2011

### micromass

No, try to say only something about the set {f(1),...,f(k)}. What do you know about this set if f is a function?? Injective?? Increasing??

5. Aug 20, 2011

### AkilMAI

that 1=f(1),2=f(2)...........n=f(k)
f(i)=f(j) where f(1)=<f(i)=<f(j)=<f(k) if i=j 1=<i=<j=<n and
f(1)<f(2)<f(3).....<f(k).....if 1<2....<n
is this correct?

6. Aug 20, 2011

### micromass

for what is that an answer??

7. Aug 20, 2011

### AkilMAI

Function: 1=f(1),2=f(2)...........n=f(k)
Injective: f(i)=f(j) where f(1)=<f(i)=<f(j)=<f(k) if i=j 1=<i=<j=<n and
Increasing: f(1)<f(2)<f(3).....<f(k).....if 1<2....<n
is this correct?

8. Aug 20, 2011

### micromass

The function bit is not correct.

If f is a function, what can {f(1),...,f(k)} be?

9. Aug 20, 2011

### AkilMAI

the range.
Are the other parts ok?

10. Aug 20, 2011

### micromass

Yes, that seems good.

11. Aug 20, 2011

### AkilMAI

should I write the function bit like this 1->f(1)....?

12. Aug 20, 2011

### micromass

that would be better

13. Aug 20, 2011

### AkilMAI

ok ....thank you