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.

15776 questions
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Is it legitimate to define a function in a proof?

I am working on a lemma with proof by mathematical induction. To make my proof easier to parse, I want to define a function - it is likely I will not refer to this function anywhere else in the document. Is it legitimate to define a function in a…
David Poxon
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Can I say $x>0 \implies x\ge0$?

By the logic, I can understand that if $P$ is true, $P \lor Q$ is also true whatever $Q$ is. Since $x\ge 0 \iff (x>0 \lor x＝0)$, if I know $x>0$, can I conclude $x\ge 0$? Sorry for some sort of stupid question.
Sizuku25252
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Is it allowed prove the theorem with lemma first

Sorry for this silly question, because I'ven't studied proof theory. Maybe I have a little misconception about this. Anyway, Suppose I have to prove a theorem. The theorem has the highest generalization, which is we just can't prove the theorem…
user516076
  • 2,200
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Tiling a square problem

Question: A 2018 x 2018 square is tiles with some 4 x 1 rectangles and some 2 x 2 squares. One of the 4 x 1 rectangles is removes and replaced with a 2 x 2 square. Is it still possible to tile the original 2018 x 2018 square with the new set of…
EricGunter7055
  • 105
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Prove if $k$ is an integer, then $k^2 - 3k$ is an even integer

Prove if $k$ is an integer, then $k^2 - 3k$ is an even integer Im having some trouble with this proof. Im using proof by contrapositive (if $k^2 - 3k$ is odd integer then $k$ is not an integer), and so I set $k^2 - 3k = 2k + 1$ and rearranged it…
user677216
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Proof by cases that $x \le |x|$?

Proof by cases that $x \le |x|$? May I have an example?
user63915
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Tilling chessboard by L shaped tiles, to cover all white cells

Consider an N x N chessboard whose top-left corner is colored white. And we have to cover all white cells. The only tool we have are black L-shaped tiles each of which covers 3 unit cells. Formally, each tile covers 3 unit cells satisfying the…
Mohit
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Understanding Proof by Contrapositive

This is a question from my textbook, and I'm pretty sure I have the answer, but I am having trouble writing out what I am thinking. Prove: If $n$ is an integer and $3n+2$ is odd, then $n$ is odd. Contrapositive: If $n$ is even, then $3n+2$ is…
Ishmael
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help for proving an equation by induction

For this equation: $$-1^3+(-3)^3+(-5)^3+\ldots+(-2n-1)^3=(-n-1)^2(-2n^2-4n-1)$$ how can I prove this by induction? When I set $n = 1$ for the base case I got: $$-1^3 + (-3)^3 + (-5)^3 + \ldots + (-3)^3 = -28$$ but am having trouble with the…
math12341123
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Binary Connective Proofs

I’m working to understand proofs that involve showing the completeness (or incompleteness) of a set of binary connectives and I have run into some confusion. Alright, so I believe I understand how to show a set of binary connectives is complete; you…
Amateur Math Guy
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Prove using induction: $n^2 - 7n + 12 \geq 0$, where $n \geq 3$

Does this work as an inductive prood? It feels like of weird, I might be doing the basis step twice unecessarily...
papercuts
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3 answers

Consider $A = \{x \in \mathbb{Q} \mid x < \pi \}$. Formally prove that $\sup A = \pi$.

I wasn't sure how to go about solving this, but I had a couple of ideas: 1.) Utilizing the fact that the rationales are a subset of the reals to say that $\sup (A) - \varepsilon < x < \pi$. However, I run into a brick wall. For this to happen,…
Brandon Evans
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Proof involving inequalities and subsets

If A is the set of ordered pairs defined by $x^2 +4y^2 < 1$ and B is the set of all pairs defined by $y< 1/2$ then prove that A is a proper subset of B. Im new to proof and not sure how this should be written, but i aimed to show all the solutions…
Carlos Bacca
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Proving for all x there is a y such that Q

The specific problem I have is $\forall x\in[0,1), \exists y\in[0,1) \ $ such that $ x
user2793618
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Proof: $x (y - x + 1) > y$ if $y > x$

I'm working on a computation which depends on the idea that given two natural numbers $x$ and $y$ where $y > x$, the product $x(y - x)$ will always be greater than $y$. Is there a proof of this ? My elementary math is a bit rusty. The simple…
Saad Farooq
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