How can suppose, let, and consider be used in proof writing?

In summary, there are no specific rules for using words like "suppose", "let", and "consider" in proofs. These words are simply used to establish the hypothesis or starting point of the proof and can be used interchangeably.
  • #1
mlarson9000
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Homework Statement


This isn't a homework problem, but I just had a general question about the language of writing proofs. I often see words like "suppose", "let", and "consider" in proofs. Could someone explain to me if there are rules to applying these? It doesn't seem like they are just randomly thrown into start off a proof.


Homework Equations





The Attempt at a Solution

 
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  • #2
I don't know of any formal rules. English has a lot of flexibility. All three of those words could be used to accomplish the same thing:

Suppose A is a right triangle, then the Pythagorean theorem...

Let A be a right triangle, then the Pythagorean theorem...

Consider a right triangle A. The Pythagorean theorem...

They all three serve to establish the hypothesis that A is a right triangle.
 

1. What is "basic proof writing"?

Basic proof writing is a fundamental skill in mathematics and other scientific fields. It involves using logical reasoning and mathematical principles to prove the validity of a statement or theorem.

2. What are the key elements of a basic proof?

A basic proof typically includes an assumption or hypothesis, a series of logical steps or arguments, and a concluding statement that shows the validity of the original hypothesis.

3. How do I begin writing a basic proof?

The first step in writing a basic proof is to clearly state the hypothesis or statement that you are trying to prove. Then, you can begin to use logical reasoning and mathematical principles to build your argument.

4. What are some common mistakes to avoid when writing a basic proof?

Some common mistakes in basic proof writing include using incorrect or incomplete logical steps, assuming the conclusion instead of proving it, and not clearly defining or stating the hypothesis.

5. Are there any tips for improving my basic proof writing skills?

Practice is key when it comes to improving your basic proof writing skills. You can also try breaking down complex proofs into smaller, more manageable steps, and seeking feedback from peers or instructors to identify any areas for improvement.

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