Questions tagged [proof]
The proof tag has no usage guidance.
46
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How can I prove that the sequence converges to $\log(2)$?
There are two rational sequences.
One of them describes convergents of the continued fraction for $\log(2)$.
Its Mathematica code is as follows:
...
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3
votes
2
answers
232
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Linear dependence of two vectors is a necessary and sufficient condition for an equality
This is an example in the textbook.
To prove: for any real number** $a_1, a_2, \cdots, a_n, b_1, b_2, \cdots b_n$, linear dependence of the two vectors $\left(a_1, a_2, \cdots, a_n\right)$ and $\left(...
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The integer ababab (a,b>0) is always divisible by 7, without remainder
The integer $ababab$ $(a>0,b>0)$ is always divisible by $7$, without rest.
I tried to prove this by:
...
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-1
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1
answer
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Why can't Mathematica confirm this simple identity? [closed]
It is well known that for positive integer $n\geq2$,
$$
\sum_{k=1}^{n-1} \frac{(-1)^{k-1}(k-1)!^2}{(n^2-1^2)\ldots(n^2-k^2)}=\frac{1}{n^2}-\frac{2(-1)^{n-1}}{n^2 \binom{2n}{n}}.
$$
This identity ...
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4
answers
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Maximum sum of product of two arrays [closed]
Any math proof for maximum sum of product of two array achieved by maximum times maximum
A = {5, 2, 1, 3};
B = {1, 2, 3, 4};
...
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1
vote
1
answer
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Why does Mathematica not return "True" for Correlation function equality expression?
I wish to check the invariance property of correlation. As described in this wiki section Wiki - Mathematical Properties of Correlation. A quote from the Wiki page I wish to test is below.
That is, ...
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votes
1
answer
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Proving an integral identity [closed]
Assuming $f$ is continus on $[0,\pi]$, show that
$$\int_{0}^{\pi }xf(\sin x)dx=\frac{\pi }{2}\int_{0}^{\pi }f(\sin x)dx$$
I tried to demonstrate it using integration by parts, but I did not succeed.
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What is the proper way to feed this function as input and test if my statement is true?
$f(S)$ = {$n∈N$: $n=m²$ for $m∈S$}
$S$ = $1,2,3$
Square each element in S
Now, $S= 1, 4, 9$
All elements in $S$ are counting from $1$ to $N$. In this case $N=3$
$f(S)$ = {$n∈N$: $n=m²$ for $m∈S$} ...
- 101
0
votes
1
answer
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Prove Geometry automatically [closed]
If given a geometric problem, can Mathematica solve it automatically? Is there any software that can solve geometry problems automatically?
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1
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Trigonometric identity not simplifying
I have a pair of numbers {x,y} (Reals or Integers) for which I want to confirm symbolically that
ArcTan[y/x]+ArcTan[x/y]==Pi/2
Here is my attempt:
...
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1
vote
1
answer
74
views
Can Mathematica check if I correctly applied an algebraic transformation?
Mathematica has tons of functions to perform algebraic manipulations. But is there a way to use it to check if I didn't make mistakes in my own algebraic manipulations.
As a real world example:
[...
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7
votes
1
answer
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Using logical equivalence to prove PL statements
I'm trying to use those Logical equivalence as axioms to prove some PL statements,
In this case I followed the examples in the documentation that didn't use the build-in logic functions$\{\text{And}[,]...
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6
votes
1
answer
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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
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0
answers
137
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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 ...
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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 ...
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1
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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
...
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4
votes
1
answer
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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
...
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1
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1
answer
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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 ...
- 141
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votes
1
answer
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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:
...
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9
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1
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213
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Proving uniqueness of group identity element
Start, as in the Mathematica 11.3 documentation, with:
...
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2
votes
1
answer
120
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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 ...
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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, ...
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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 \...
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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 ...
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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
...
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6
votes
1
answer
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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.
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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 ...
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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
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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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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 ...
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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 ...
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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 ...
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2
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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. ...
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2
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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 ...
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0
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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)....
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1
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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 $S^2$
...
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answer
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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 ...
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3
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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.
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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 ...
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How can I prove an equation has a certain number of real roots?
I have this code
...
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3
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382
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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.
...
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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 ...
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0
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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 ...
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votes
3
answers
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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-...
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1
answer
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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 $...
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7
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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 ...
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