# Questions tagged [proof]

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### Proving the hairy ball theorem using xAct

I would like to formally prove the hairy ball theorem in Mathematica, initially just for $S^2$, and then see about generalizing. An approach I thought about to use the xAct package to define $S^2$ ...
3answers
916 views

### Proving (or at least 'being told by Mathematica') that Sqrt[2] is irrational?

I realize that Mathematica is not specifically an automated theorem prover. However, this article: http://www.wolfram.com/products/mathematica/newin6/content/EquationalTheoremProving/ Suggests that ...
1answer
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1answer
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### Solving functional equations in Mathematica

I am trying to solve functional equations in Mathematica, but got nowhere. Just a simple example: $$f(x+y)^2=f(x)^2+f(y)^2$$ for all $x,y \in R$, assuming f is a real-valued function. How should I ...
1answer
204 views

### Fundamental question about capabilities of Mathematica to represent abstract mathematics [closed]

I have an fundamental question about what Mathematica can and cannot do. I have a book which presents a certain physical theory in an axiomatic manner. The axioms make heavy use of mathematics. Some ...
2answers
1k views

### How can I calculate the limit without using the L'Hopital's rule

I need to prove this limit without using the L'Hopital's rule: $$\lim_{x\to 0} \frac{(1+a\,x)^{1/4} - (1+b\,x)^{1/4}}{x} = \frac{a-b}{4}$$ How can I do it in Mathematica?
3answers
361 views

### Proving a recurrence in Mathematica

I have $$j_n=\int_0^1 x^{2n} \sin(\pi x)dx.$$ How do I show that $$j_{n+1}= \frac{1}{\pi^2}(\pi- (2n+1)(2n+2)j_n)\, ?$$ I keep getting a recurring integration by parts and I can't simplify it. ...
1answer
213 views

### FindEquationalProof with Logic in Wolfram Mathematica

I try to "make" proof in Wolfram Mathematica. Thats a proof: if a->b and b->c then a->c I tried ...
2answers
185 views

### Proving that Reverse[Reverse[x]]]=x

It is clear that for any list $x$, Reverse[Reverse[x]]=x. I want to have Mathematica tell me that this is true. I have tried entering ...
1answer
598 views

### How to extract steps from FullSimplify? [duplicate]

The answer proposed to the original question doesn't solve it, I need to understand the results of TraceInternal when used on FullSimplify as a sequence of steps, which has not been resolved for me. ...
1answer
90 views

### FindEquationalProof to prove divisor theorem

I'm trying to implement proofs of concepts for Equational Proofs on some basic number theory theorems. One such example is: "let a and b be positive integers and let d = gcd (a, b). If t divides ...
1answer
158 views

### Implementing the field axioms with FindEquationalProof?

I am fiddling around with FindEquationalProof, currently trying to prove some basic statements for fields. I have a set of axioms which almost constitutes the field theory axioms: ...
0answers
178 views

### Theorem Proving

It's a hard for me to write english so I'll try to go straight to my problem. There is abstract predicate f, that takes two parameters. There are also two other ...
0answers
243 views

### Can I define an axiomatic (Boolean algebra) system and prove theorems using Mathematica?

The general question is Can I define an axiomatic system and prove theorems using Mathematica? The more concrete one is about Boolean algebra. I consider this axiomatic Boolean algebra system (wiki)....
2answers
304 views

### Using Mathematica to confirm Bernoulli's inequality

I have several challenges that I want to confirm is true. I have chosen this one because it is rather simple (proof by induction). There are times when I do not want to spend ages trying find proofs. ...
1answer
756 views