Tagged Questions
8
votes
1answer
159 views
Function mapping challange
For a given set $A=\{1, 2, 3, 4, \ldots, n\}$, find the number of non-constant
mappings (associations ) $f$ from $A$ to $A$ such that $f(k) \leq f(k + 1)$
and $f(k) = f(f(k + 1))$.
This is ...
5
votes
3answers
134 views
Looking for a function $f$ such that $f(i)=2(f(i-1)+f(\lceil i/2\rceil))$
I'm looking for a solution $f$ to the difference equation $$f(i)=2(f(i-1)+f(\lceil i/2\rceil))$$ with $f(2)=4$. Very grateful for any ideas.
PS. I've tried plotting the the initial values into ...
5
votes
1answer
102 views
What function $f$ such that $a_1 \oplus\, \cdots\,\oplus a_n = 0$ implies $f(a_1) \oplus\, \cdots\,\oplus f(a_n) \neq 0$
For a certain algorithm, I need a function $f$ on integers such that
$a_1 \oplus a_2 \oplus \, \cdots\,\oplus a_n = 0 \implies f(a_1) \oplus f(a_2) \oplus \, \cdots\,\oplus f(a_n) \neq 0$
(where the ...
3
votes
3answers
338 views
Domain, codomain, and range
This question isn't typically associated with the level of math that I'm about to talk about, but I'm asking it because I'm also doing a separate math class where these terms are relevant. I just want ...
3
votes
2answers
101 views
Prove $f(S \cup T) = f(S) \cup f(T)$
$f(S \cup T) = f(S) \cup f(T)$
f(S) encompasses all x that is in S
f(T) encompasses all x that is in T
thus the domain being the same, both the LHS and RHS map to the same ys, since the function ...
3
votes
1answer
216 views
What does the notation $|f(A)| = X$ mean?
$A$ is a set and so is $B$.
$f$ is a function $A \to B$.
I have a math question that asks about $|f(A)|$. What does the notation $|\cdot |$ mean?
2
votes
3answers
317 views
calculating unique value from given numbers
let's say I have some (n) random numbers 12, 13, and 18. I want to calculate some unique value from these three such that if I change their order 13, 12, 18 or 18, 12, 13..whatever order they are in, ...
2
votes
3answers
103 views
Is $f:\mathbb{Z}_{30}\longrightarrow\mathbb{Z}_{30}$ defined by $f([a])=[7a]$ well defined?
To tell the truth, I'm not even sure what this means.
The professor gave an example saying that $\mathbb{Z}_m=\{[0],[1],[2],\dots,[m-1]\}$, and I sort of understand that.. but I have no idea what ...
2
votes
4answers
65 views
Solve for $x$: $4x = 6~(\mod 5)$
Solve for $x$: $4x = 6(mod~5)$
Here is my solution:
From the definition of modulus, we can write the above as $ \large\frac{4x-6}{5} = \small k$, where $k$ is the remainder resulting from ...
2
votes
1answer
89 views
Are there straightforward methods to tell which function has fastest asymptotic growth without a calculator?
For example, suppose I wanted to determine which of the following has the fastest asymptotic growth:
$n^2\log(n)+(\log(n))^2$
$n^2+\log(2^n)+1$
$(n+1)^3+(n-1)^3$
$(n+\log(n))^22^{100}$
Are there ...
2
votes
2answers
3k views
How to determine if this function is one-to-one, onto, or bijection?
I have a function $f_2: \mathbb Z \times \mathbb Z \to \mathbb Z $ defined by $f_2(m,n)=m^2+n$.
How do I know if it is one-to-one, onto or both?
What I am most confused about is what $\mathbb Z ...
2
votes
3answers
72 views
Counting 1:1 and onto functions
I'm faced with the following questions:
1) How many functions are there from a set of size 3 to a set of size 5? How many of them are 1-to-1?
2) How many functions are there from a set of ...
2
votes
1answer
42 views
Composition of two functions in $\mathbb{Z^2}\to \mathbb{Z^2}$
I need to find the composition of a function and its inverse so I have the identity function in return. My problem is that I don't seem to undestand how to proceed algebraically.
I have a function ...
2
votes
1answer
47 views
Showing a bijection with a contraction
I have the function $F(x) = x + f(x)$ where $f(x)$ is a contraction: $|f(x)-f(y)| \leq \alpha|x-y|$ for some $0 < \alpha < 1$ and all $x, y \in \mathbb{R}$
I want to show that $F$ is a ...
1
vote
7answers
335 views
Is there any function where $f \circ f = f$ but $f(0) = 1$
Other than the identity function, is there any function where $f \circ f = f$?
$f(0)$ also has to return 1.
It must has something to do with the exponent 0 to a some coefficient...
Anyone could give ...
