MHB A Surjective function from [0,1]\{1/2} to [0,1]

Click For Summary
The discussion revolves around the challenge of finding a surjective function from the interval [0,1] excluding 1/2 to the interval [0,1], with the condition that if f(a) > f(b), then a > b. The original poster expresses difficulty in solving this problem without using cardinality arguments. A participant suggests considering an increasing sequence approaching 1/2 and questions the behavior of the function at that limit. The conversation highlights the complexities of defining such a function under the given constraints.
Ella1
Messages
2
Reaction score
0
Hello guys! I'm taking Discrete Mathematics this semester and I got this question in one of my homework tasks.
I've tried thinking about the solution over and over but can't seem to come up with anything..
The question goes like this: Is there a Surjective function from [0,1]\{1/2} to [0,1] such that if f(a)>f(b) that means that a>b?
I must mention that sadly I cannot use any arguments involving cardinality..
Any clue that might help will save my life!p.s Sorry for my poor English :)!
 
Physics news on Phys.org
Ella said:
Hello guys! I'm taking Discrete Mathematics this semester and I got this question in one of my homework tasks.
I've tried thinking about the solution over and over but can't seem to come up with anything..
The question goes like this: Is there a Surjective function from [0,1]\{1/2} to [0,1] such that if f(a)>f(b) that means that a>b?
Hi Ella, and welcome to MHB!

Suppose that $(x_n)$ is an increasing sequence in $[0,1/2)$, with $\lim_{n\to\infty}x_n = 1/2.$ What can you say about the point $\lim_{n\to\infty}f(x_n)$? Can it be in the range of $f$?
 

Thread 'A variant of the Monty Hall problem'

There is a nice little variation of the problem. The host says, after you have chosen the door, that you can change your guess, but to sweeten the deal, he says you can choose the two other doors, if you wish. This proposition is a no brainer, however before you are quick enough to accept it, the host opens one of the two doors and it is empty. In this version you really want to change your pick, but at the same time ask yourself is the host impartial and does that change anything. The host...
View full post »

Similar threads

I Create a surjective function from [0,1]^n→S^n
  • · Replies 8 ·
Replies
8
Views
3K
I What is the Definition and Understanding of Surjective Functions?
  • · Replies 1 ·
Replies
1
Views
1K
MHB How Can We Prove Two Open Intervals in $\mathbb{R}$ Are Equinumerous?
  • · Replies 10 ·
Replies
10
Views
3K
MHB Proving Existence of Surjective Function F from P(N)\N to P(N)
  • · Replies 1 ·
Replies
1
Views
2K
I Cantor's decimal proof that (0,1) is uncountable
  • · Replies 9 ·
Replies
9
Views
5K
Does there exist a surjection from the natural numbers to the reals?
  • · Replies 4 ·
Replies
4
Views
4K
Injection from finite set to equally sized set is surjection
  • · Replies 13 ·
Replies
13
Views
4K
MHB Find Cov(Z,W) with E(X^2)if X is N(0,1)
  • · Replies 3 ·
Replies
3
Views
2K
MHB Partial Order Relation on a Functions Set
  • · Replies 3 ·
Replies
3
Views
2K
Prove bijection from (0,1] to (0,1)
  • · Replies 4 ·
Replies
4
Views
2K