Are Books Necessary to Understand Mathematical Proofs?

In summary, proofs are necessary in various fields as they provide evidence and reasoning to support a claim or theory. They are not only used in mathematics and logic, but also in science, philosophy, and law. The process of constructing a proof involves breaking down the statement into smaller pieces and using logical reasoning and evidence to support each piece. Not all statements require a proof, and a proof can never be considered absolute, but it can be considered strong or convincing if it is based on sound logic and supported by solid evidence.
  • #1
hellbike
61
0
I'm looking for book about making proof.

Is this kind of book even required to understand proofs? Is there some special theory behind proofs, or books about proofs just provide examples, and are more like "math for dummies" ?

I'm not sure if it's proper to use that kind of book, should i figure everything out by myself from books about standard math topics (like calculus) ?
 
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  • #2
How to Prove It: A Structured Approach by Daniel J. Velleman

or probably a better introduction if you can afford it

Discrete Mathematics with Applications by Susanna S. Epp
 

1. What are proofs and why do we need them?

Proofs are a way of demonstrating the truth or validity of a statement or argument. They are necessary because they provide evidence and reasoning to support a claim or theory, helping to establish its credibility and convince others of its truth.

2. Are proofs only used in mathematics and logic?

No, proofs can be used in various fields such as science, philosophy, and law. In science, proofs are used to support theories and hypotheses, while in philosophy, proofs are used to support philosophical arguments. In law, proofs are used to establish the guilt or innocence of a defendant.

3. What is the process of constructing a proof?

The process of constructing a proof involves identifying the statement or claim to be proven, breaking it down into smaller, more manageable pieces, and then using logical reasoning and evidence to support each piece until the entire statement is proven.

4. Do all statements require a proof?

No, not all statements require a proof. Some statements are self-evident or can be accepted without proof, while others may be based on assumptions or beliefs that cannot be proven.

5. Can a proof ever be considered absolute?

It is not possible for a proof to be considered absolute as it is always subject to potential errors or flaws in reasoning. However, a proof can be considered strong or convincing if it is based on sound logic and supported by solid evidence.

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