Property of a sequence for a function.

[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.

 

[micromass]

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.

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.

 

[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

 

[micromass]

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

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??

 

[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?

 

[micromass]

for what is that an answer??

 

[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?

 

[micromass]

The function bit is not correct.

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

 

[AkilMAI]

the range.
Are the other parts ok?

 

[micromass]

Yes, that seems good.

 

[AkilMAI]

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

 

[micromass]

that would be better

 

[AkilMAI]

ok ...thank you