Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [proof-writing]

For questions about the formulation of a proof. This tag should not be the only tag for a question and should not be used to ask for a proof of a statement.

Questions with this tag are about the presentation of a mathematical proof. Questions might include:

  • Should I include [x-mathematical detail] at [y-part of this proof]?
  • Is the following a sufficient proof of [x-mathematical tidbit]?
  • I have written the following proof, could I somehow improve it, does it have good flow/can I improve readability?

But this tag is not for asking someone else to write a proof for you, or for how to answer some question. Questions such as: My professor asked me to prove the Pythagorean theorem and I don't know how to begin are not to have this tag.

This tag is intended for use along with other, more "mathematical" tags. A question about the writing of a proof in abstract algebra, for example, should have as well. This tag can be used along with the proof verification tag.

See here for a useful set of guidelines for writing a solution.

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Similar Matrices and Nullspace Proof

Prove that if A and B are similar matrices, the dim $Null(A)$ = dim $Null(B)$ I'm not really sure where to start for this problem. Any help would be appreciated. Thanks
Ian Murphy
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Prove an existential quantifier goal by assuming there exists an arbitrary value that makes the expression true.

I'm trying to prove the following: Suppose { A$_{i}$ | i $\in$ I } is an indexed family of sets and I $\neq$ $\emptyset$. Prove that $\cap$$_{i \in I}$A$_{i}$ $\in$ $\cap$$_{i \in I}$$\mathcal{P}(A_{i})$. I first analysed the logical structure…
jviotti
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Simple Linear Algebra Proof - Determinants

Prove or disprove the following statement: If R is the RREF of A, then det A = det R. So far, I think that this is true, considering A and R are row equivalent, and that the determinant changes as we row reduce in order to compensate for the…
Ian Murphy
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Basis and vector spaces with change of coordinates

Let $B = \{v_1,...,v_n\}$ be a basis for a vector space $V$ and let $u_1,..., u_k \in V$. If $\{[u_1]_B,...,[u_k]_B\}$ is linearly independent in $\mathbb{R^n}$, then $\{u_1,...,u_k\}$ is linearly independent in $V$. For this question, I must prove…
Ian Murphy
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Linear Algebra Simple Proof

Prove the following result, or provide a counterexample to disprove it. There is a vector space which contains exactly 2 vectors within it. For this question, I'm not sure where to start. To me this statement seems to be true, since I only have…
Ian Murphy
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How would I say that two elements do not belong to the same set?

Let's say I have two lists, X, Y. X = {limegreen, forestgreen, seagreen}, Y = {babyblue, navyblue, ultramarineblue} And I have the elements $d_0, d_1, d_2, ..., d_n$. I want it so no two consecutive elements are from the same set. I know I can…
Michael Nguyen
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Linear Algebra Proof with Ranks

Here is the proof that I am trying to show. Let A be an m x n matrix in RREF. If rank(A) = r < m, then A must have at least one row of zeroes. So far, I've noticed that is true, and that if for example, there are 5 equations, but only 4 leading…
Ian Murphy
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Prove that a rational number minus an irrational number must be irrational.

Please help with this homework problem I have! I don't know how to prove this.
Chris
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Prove $\sin x=3x-2$ has only one real solution

Obviously you can draw a graph, but how would you prove this with calculus?
Jim
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For any $ n \in \mathbb N$, there is an odd integer m such that $n^2 < m < (n+1)^2.$

Thanks for the help for the previous proof. Now I am stuck on this statement I need to prove. For any natural number $n$ there is an odd integer $m$ such that $n^2 < m < (n+1)^2$. I got to: $$n^2 < 2n+1 < n^2 + 2n + 1$$ I am not sure how to…
Brenda
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Cardinality problem with multiple sets

What we are given in part A) This is part B) What we are asked to prove My best idea is that if you evaluate what the proof is, it turns into what is given except A is Ai and B is Ai+1 and all the way to An. On the other side, its just…
k9b
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How to formally state and prove vacuous truth?

How to show in a proof that a statement is vacuously true because "if $\alpha$ then $\beta$", and also prove $\alpha$ is false, in a formal way? and also particularly, how to structure such proofs? For example to vacuously prove $\forall A.…
MasterMastic
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Help on the Inclusion Exclusion principle and explaining cardinality

I want to prove the inclusion exclusion principle: |A∪B|=|A|+|B|−|A∩B| where A and B are finite sets. However I'm confused about one thing. I've learned that two cardinalities are equal if there is a bijection over them... So how would I apply that…
k9b
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Proving a surjection. Clarification

I just want to make sure this is all correct. So my definition of a function $f:A\to B$ being a surjection is: For all $b \in B$, there exists an $a \in A$ such that $f(a) = b$. Now the question: Let $f: \mathbb N \to \mathbb Z \\ n \mapsto…
k9b
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How to prove this thing from Graph Theory?

How to prove that if we have two DAGs (Directed Acyclic Graph) D1 , D2 and if D1+ = D2+ then (D1)= (D2). D+ means that in this graph there is a positive length path. Example: D grapth may have point A and B, but in D+ graph these two are connected.…
Misho Metreveli
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