How to Prove Points in an Open Interval are of a Certain Form?

In summary, the conversation is about proving that the points in the open interval (a,b) can be written in the form a + t(b-a) for some 0 < t < 1, and vice versa. The person asking the question is seeking confirmation that their interpretation is correct before their homework deadline. They also jokingly offer to pay the expert for their quick response.
  • #1
JG89
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Homework Statement



Prove the points of the open interval (a,b) are those of the form a + t(b-a) for 0 < t < 1.

Homework Equations





The Attempt at a Solution



I'm interpreting this as asking me to prove that if x is in (a,b), then x can be written as
a + t(b-a) for some 0 < t < 1. Conversely, it's asking me to prove that if x = a + t(b-a) with 0 < t < 1, then x is in (a,b).

Is this interpretation correct?
 
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  • #2
Please answer quick. This is a homework question due in a couple hours. I've already finished the question and my problem set, but I want to make sure that I proved the correct thing!
 
  • #3
Yes, your interpretation is correct.

Sorry I couldn't get this to you sooner but I was busy with something I am actually paid to do.
 
  • #4
but I was busy with something I am actually paid to do.

I'll pay you double! Just kidding, thanks for the response. It came in time :)
 

FAQ: How to Prove Points in an Open Interval are of a Certain Form?

What is the purpose of interpretation of question?

The purpose of interpretation of question is to understand the meaning and intention behind a question. It involves analyzing the words and context of the question to determine what information is being sought.

How is interpretation of question different from answering a question?

Interpretation of question involves understanding the meaning and intention of a question, while answering a question involves providing a response or solution based on that understanding.

What are some common methods for interpreting a question?

Some common methods for interpreting a question include breaking down the question into smaller parts, considering the context and tone of the question, and asking for clarification if needed.

Why is interpretation of question important in scientific research?

Interpretation of question is important in scientific research because it ensures that the research is focused and relevant. It also helps to avoid miscommunication and ensures that the results of the research are accurate and meaningful.

Can interpretation of question be subjective?

Yes, interpretation of question can be subjective to some extent. Different individuals may interpret a question differently based on their own perspectives and biases. However, in scientific research, interpretation of question should strive to be as objective and unbiased as possible.

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