Provide an example or prove it wrong

  • Thread starter Quinzio
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In summary, a continuous function g: Q --> R such that g(0)=0 and g(1)=1, but there does not exist any x in Q such that g(x)=1/2 can be demonstrated by the function f(x) = x^2, which satisfies the given conditions. It is not necessary to prove that no such example exists.
  • #1
Quinzio
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Homework Statement


A continuous function g: Q --> R such that g(0)=0 and g(1)=1, but there does not exist any x in Q such that g(x)=1/2

Homework Equations


Number sets, basic number theory

The Attempt at a Solution


The function could be [tex]f(x) = x^2[/tex]

since

[tex]f(0) = 0[/tex]

[tex]f(1) = 1[/tex]

[tex]f(x) = 1/2[/tex]

here it looks like [tex]x[/tex] must be an irrational. One could refer to the demonstration that the diagonal of a square is an irrational.

Is it enough as a prove ?
 
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  • #2
Quinzio said:

Homework Statement


A continuous function g: Q --> R such that g(0)=0 and g(1)=1, but there does not exist any x in Q such that g(x)=1/2


Homework Equations


Number sets, basic number theory



The Attempt at a Solution


The function could be [tex]f(x) = x^2[/tex]

since

[tex]f(0) = 0[/tex]

[tex]f(1) = 1[/tex]

[tex]f(x) = 1/2[/tex]

here it looks like [tex]x[/tex] must be an irrational. One could refer to the demonstration that the diagonal of a square is an irrational.

Is it enough as a prove ?

Going by the title of your thread, you need to do one of two things:
1) Provide an example for which the conditions are met.
2) Prove that no such example exists.

f(x) = x2 is an example that works, so you don't need to prove anything.
 
  • #3
Mark44 said:
Going by the title of your thread, you need to do one of two things:
1) Provide an example for which the conditions are met.
2) Prove that no such example exists.

f(x) = x2 is an example that works, so you don't need to prove anything.

Ok, I see.

Thanks for your contributions.
 

1. Can you give an example to support your claim?

Yes, for example, in the field of medicine, a study was conducted to prove the effectiveness of a new drug. The results showed that the drug had a significant impact on treating the targeted disease, providing evidence to support the claim.

2. How do you prove something wrong?

To prove something wrong, you can conduct experiments or gather data that contradicts the initial claim. This can be achieved through thorough research, critical thinking, and analysis of evidence.

3. Is providing an example enough to prove something?

Providing an example is a good start to support a claim, but it is not always enough to prove something. It should be accompanied by solid evidence and data to strengthen the argument and make it more convincing.

4. What makes a proof valid?

A valid proof is supported by evidence, data, and logical reasoning. It should also be replicable and withstand scrutiny from other scientists in the field. A valid proof is objective and can be accepted by the scientific community.

5. Can something be proven wrong in science?

In science, claims and theories are subject to change and can be proven wrong through further research and evidence. This is what makes the scientific method so valuable, as it allows for continuous improvement and advancement in our understanding of the world.

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