Questions tagged [proof]

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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 ...
2
votes
0answers
70 views

How to prove subspaces of function spaces?

In teaching Linear Algebra, I would like to prove or disprove whether a nonempty subset of a vector space, is a subspace. For this, I would show that the subset is closed under both addition and ...
1
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0answers
52 views

FindEquationalProof with implications

Motivated by this question in mathematics, my Mathematica question is essentially this one, but alas the answer to that isn't quite adequate. I'm not interested in verifying that a proof is valid or ...
5
votes
1answer
132 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 ...
4
votes
1answer
75 views

What does this graph mean?

Mathematica 11.3.0 includes a new command FindEquationalProof having good prospects. Studying it, I consider a somewhat modified example from the help ...
1
vote
1answer
40 views

Proofs and exponents to the N power

I'm still a beginner at Mathematica and I'd like to understand how to use it for proofs. Here is a simple one on exponent properties (a*b)^n == a^n*b^n I tried ...
3
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0answers
106 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: ...
9
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1answer
139 views

Proving uniqueness of group identity element

Start, as in the Mathematica 11.3 documentation, with: ...
1
vote
1answer
89 views

Two Dimensional BVP

I am having a hard time in how someone could solve ${d^2V}/{d^2y^2}$+${d^2V}/{d^2x^2}$=0 with the following boundary conditions: V=0 when y=0, V=0 when y=a, V=$V_o$(y) when x=0, V->0 as x-> infinity ...
2
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1answer
78 views

When Reduce yields False for a system of inequalities, can I take this as a formal proof? [closed]

As part of the proof of a proposition in an economics paper, I need to show that a system of inequalities in four variables is inconsistent. Because the system is complicated, I cannot show this ...
1
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3answers
78 views

Can you determine values in a set of integers from a known set sum and set product

Question: There is a set of numbers defined as {A, B, C, D, E} The sum of the set is 49 (A+B+C+D+E = 49) The product of the set is 13000 (ABCDE = 13000) Can you determine the values of A, B, ...
4
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1answer
654 views

Proof of the Dirac-$\gamma$ matrices identity

Given the matrices $\gamma_{k}=\begin{bmatrix} O & -i\sigma_{k}\\ +i\sigma_{k}& O \end{bmatrix}$ where $\sigma_{k}$ is the $k^{th}$ Pauli matrix $\gamma_{4}=\begin{bmatrix} I^{2} &0 \...
2
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2answers
749 views

How to “Prove” this summation result?

I have this messy function with $n$, $k$, $i$ integers: $$ r(\rm n,k)=\frac{k 2^{1-2 \rm{n}} (2 k)! (-2 k+2 \rm{n}+1) (2 \rm{n}-2 k)!}{(k!)^2 \left(1-4 (i-k)^2\right) ((\rm{n}-k)!)^2} $$ I want to ...
4
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0answers
92 views

How to use Resolve to prove ForAll function

I want to prove that ∀n ∈ N,Mod[9^n - 8 n - 1, 64] == 0 I think I should use Resolve to prove it ...
5
votes
1answer
475 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. ...
9
votes
2answers
378 views

Symbolically prove that two expressions are identical

I encountered this problem when trying to reproduce the result of this paper. (The relevant parts are all included in the preview i.e. the 1st page of the article. This link is just given as ...
5
votes
2answers
181 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 ...
0
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2answers
87 views

How to prove that an equation can be divided by any n?

I'm new to Mathematica and came across with the problem. I can't prove that (for example) 2*n is always even no matter what n is....
5
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0answers
170 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 ...
6
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1answer
198 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 ...
17
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3answers
877 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 ...
4
votes
2answers
289 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. ...
2
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2answers
115 views

Performing an inductive proof

I have an expression which depends on a variable n and am certain it evaluates to 1 for all n with n=1/2,1,3/2,... I want to do an inductive proof that this is true but the actual formula is too ...
5
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0answers
233 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 (...
33
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1answer
1k views

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 $S^2$ ...
0
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1answer
2k views

Is this function convex?

How can I determine convexity of the function f = Log[ x, 1 + (x^a - 1) (x^b - 1)/(x - 1)] with the parameters $a,\,b$ belonging to the interval $(0,1)$ in ...
5
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2answers
952 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?
7
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1answer
418 views

Prove an identity in quantum harmonic oscillator

Problem: In the context of quantum harmonic oscillator the eigenfunctions are given by: $ u_n(x) = (N_n/\sqrt{b}) H_n(x/b) \exp\left[-x^2/(2b^2)\right] $, where $N_n$ is the normalization factor: $ ...
-1
votes
3answers
368 views

Find integer values of p such that $(2^p - (2^2)(3^2))/ (3^3)$ is an integer

Find integer values of p such that $(2^p - (2^2)(3^2))/ (3^3)$ is an integer.
4
votes
1answer
3k views

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 ...
3
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2answers
312 views
4
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3answers
354 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. ...
8
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4answers
2k views

How to prove an expression by method of mathematical induction?

I want to prove the expression $$1^2 + 2^2 + 3^2 + \cdots + n^2 = \dfrac{n(n+1)(2n+1)}{6}$$ by method of mathematical induction with Mathematica, but I do not know how to start. How do I tell ...
13
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0answers
494 views

Proving (self) similarity with Mathematica - Reccurrence Plots, Similarity Plots etc

I posted this question in math.se but given the sheer tumultuous number of questions that keep appearing on math.se and also given that I am trying to accomplish this in Mathematica, I thought I'd ...
11
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3answers
2k views

Using FindInstance to Prove No Solutions Exist

For a small amount of background, I am currently working on an undergraduate research project in Combinatorial Geometry and I'm working on a case analysis for embedding spherical simplicial 2-...
12
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1answer
2k views

Proving inequalities with Mathematica

Question summary: I would like to learn some tips and tricks on how to prove inequalities with Mathematica. I'm studying various inequalities in triangle that have the form $R+ar + bs\geq 0$, where $...
10
votes
7answers
3k views

Trying to prove that $x\sin(\frac{\pi}{x})\ge\pi \cos(\frac{\pi}{x})$ for $x\ge 1$

As an intermediate step, consider the function: f[x_] := x Sin[Pi/x] I want to prove that this function is increasing for $x\ge 1$. This can be done with the ...